Detection in Analytical Chemistry - American Chemical Society

Chapter 11

Critical Assessment of Detection Limits for Ion Chromatography William F. Koch and Walter S. Liggett

Downloaded by UNIV OF ARIZONA on January 7, 2013 | http://pubs.acs.org Publication Date: December 9, 1987 | doi: 10.1021/bk-1988-0361.ch011

National Bureau of Standards, Gaithersburg, MD 20899

The s t a t i s t i c a l basis for ion chromatography detection limits is investigated through the analysis of chromatograms by time series methods. Time series methods reveal two important chromatogram noise components, a cyclic variation caused by the pump and some large low-frequency variations with obscure origins. The component due to the pump can be removed from the chromatogram. The causes of the low frequency component should be investigated because these causes may not satisfy the prerequisites of s t a t i s t i c a l inference. Detection limit assessment depends on the choice of a peak detection algorithm. This algorithm must include a method for separating the low frequency component from the peak of interest and the a method for locating the peak in time. Algorithms that search for the peak in time cannot be assessed in the same way as algorithms that involve no search. This difference is discussed. The d e t e c t i o n l i m i t i n d i c a t e s the performance o f an i n s t r u m e n t a t low a n a l y t e c o n c e n t r a t i o n s . T h i s i n d i c a t i o n may be used as a g u i d e t o i n s t r u m e n t o p t i m i z a t i o n , as a gauge o f t h e s u i t a b i l i t y o f an i n s t r u m e n t f o r a p a r t i c u l a r a p p l i c a t i o n , o r as a c r i t e r i o n f o r t h e i n t e r p r e t a t i o n o f low c o n c e n t r a t i o n measurements. T h i s paper c o n c e n t r a t e s on t h e l a t t e r u s e o f d e t e c t i o n l i m i t s and expands t h e d i s c u s s i o n t o i n c l u d e a l l a s p e c t s o f s t a t i s t i c a l i n f e r e n c e on low c o n c e n t r a t i o n measurements. I n t h i s c a s e , the use o f t h e d e t e c t i o n l i m i t i s c o n f i n e d t o the measurements i n q u e s t i o n and t o t h e s t u d y a t hand. The u s e o f d e t e c t i o n l i m i t s f o r i n s t r u m e n t o p t i m i z a t i o n and f o r s u i t a b i l i t y judgments r e q u i r e s a broader p e r s p e c t i v e t h a t c o v e r s the v a r i o u s c o n d i t i o n s under which the i n s t r u m e n t might be used. The q u e s t i o n o f what d e t e c t i o n l i m i t i s a c h i e v e d i n the course of a s e t o f measurements i s b o t h c o m f o r t i n g l y s p e c i f i c and v e r y demanding. The q u e s t i o n i s s p e c i f i c i n t h a t o n l y the o p e r a t i n g c o n d i t i o n s used f o r t h e s e t o f measurements need t o be c o n s i d e r e d . F u r t h e r , good p r a c t i c e s u g g e s t s t h a t t h e s e o p e r a t i n g c o n d i t i o n s be

T h i s chapter not subject to U.S. copyright P u b l i s h e d 1988 A m e r i c a n C h e m i c a l Society

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


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l i m i t e d as much as p o s s i b l e . Thus, the amount o f d a t a t h a t i s needed i s r e l a t i v e l y modest. The a p p r o p r i a t e d a t a c o u l d be c o l l e c t e d as p a r t of the l a b o r a t o r y q u a l i t y a s s u r a n c e program. The q u e s t i o n i s demanding i n t h a t c o n c l u s i o n s w i t h b e l i e v a b l e p r o b a b i l i t i e s of e r r o r are o f t e n needed. T h i s means t h a t the measurements used t o d e r i v e p r o p e r t i e s of the e r r o r must have the same e r r o r p r o p e r t i e s as the measurements about w h i c h c o n c l u s i o n s are t o be drawn. I n o t h e r words, the unknown samples and the q u a l i t y c o n t r o l samples must b o t h r e s u l t from a measurement p r o c e s s t h a t i s under c o n t r o l . I n many c a s e s , t h i s c o n d i t i o n i s not e a s i l y a c h i e v e d because of s u b t l e d i f f e r e n c e s between the c o n d i t i o n s under w h i c h the q u a l i t y c o n t r o l measurements are made and the c o n d i t i o n s under w h i c h the r e a l measurements are made. S p e c i f i c causes of such d i f f e r e n c e s , sampleto-sample c a r r y o v e r and m e c h a n i c a l t r a n s i e n t s , are d i s c u s s e d below. T h i s paper c o n s i d e r s i o n chromatography, w h i c h i s a form o f l i q u i d chromatography based on i o n exchange s e p a r a t i o n of a n a l y t e s f o l l o w e d by c o n d u c t i m e t r i c d e t e c t i o n and q u a n t i t a t i o n (I)* In p a r t i c u l a r , t h i s paper i s based on d a t a from a Dionex Model 2 0 2 0 i . (See t h e d i s c l a i m e r . ) T h i s i n s t r u m e n t was s e t up f o r the measurement o f n i t r a t e and s u l f a t e a t c o n c e n t r a t i o n s below 1 mg/L. Except i n the cases noted below, the i n s t r u m e n t was c o n f i g u r e d as f o l l o w s : The a n i o n s e p a r a t o r column was number AS4A ( D i o n e x ) ; the e l u e n t was an a d m i x t u r e of 0.75 mmol/L NaHCC^ and 2.0 mmol/L Na2CÛ3; the f l o w r a t e was 2.0 mL/min; and the sample loop volume was 20 pL. The background conductance o f the e l u e n t was c h e m i c a l l y suppressed w i t h a h o l l o w f i b e r c h e m i c a l s u p p r e s s o r ( D i o n e x ) w i t h a 0.0125 mol/L H2SO4 régénérant f l o w i n g a t 2.8 mL/min. Under t h e s e c o n d i t i o n s , the background conductance was a p p r o x i m a t e l y 16 pS/cm. Most of t h i s paper i s r e l e v a n t t o o t h e r i o n chromatography c o n f i g u r a t i o n s . In some ways, t h i s paper i s r e l e v a n t t o a l l i n s t r u m e n t s t h a t d e t e c t a peak on a n o i s y b a s e l i n e . However, i o n chromatography d i f f e r s s u b s t a n t i a l l y from gamma s p e c t r o s c o p y and o t h e r measurement t e c h n i q u e s based on r a d i o a c t i v e decay because the randomness of r a d i o a c t i v e decay has no a n a l o g i n i o n chromatography. An i s s u e of c o n s i d e r a b l e importance i n the d i s c u s s i o n of d e t e c t i o n l i m i t s i s the c h o i c e of s o f t w a r e f o r peak i d e n t i f i c a t i o n and i n t e g r a t i o n . I n p r a c t i c e , the c h o i c e of a d a t a a n a l y s i s a l g o r i t h m can have as l a r g e an e f f e c t on the d e t e c t i o n l i m i t as the c h o i c e o f i n s t r u m e n t c o n f i g u r a t i o n . The d a t a a n a l y s i s i n t h i s paper has been done w i t h g e n e r a l purpose s t a t i s t i c a l s o f t w a r e r a t h e r t h a n w i t h one of the p r o p r i e t a r y packages a v a i l a b l e f o r i o n chromatography. G e n e r a l purpose s o f t w a r e has the advantage of a l l o w i n g f l e x i b i l i t y i n the d a t a a n a l y s i s . A l s o , g e n e r a l purpose s o f t w a r e i s based on a l g o r i t h m s t h a t are known p r e c i s e l y . U n f o r t u n a t e l y , p r o p r i e t a r y packages o f t e n do not come w i t h an e x a c t s p e c i f i c a t i o n of the a l g o r i t h m s employed. T h i s i s troublesome i n work on d e t e c t i o n l i m i t s because, as i l l u s t r a t e d below, d e t e c t i o n l i m i t s can be v e r y s e n s i t i v e t o the c h o i c e of a l g o r i t h m . Of c o u r s e , the g e n e r a l purpose s o f t w a r e used i n t h i s paper i s not as c o n v e n i e n t f o r r o u t i n e l a b o r a t o r y use, as f u l l y d e v e l o p e d , or as w e l l t e s t e d as the p r o p r i e t a r y packages a v a i l a b l e . The purpose of t h i s paper i s t o demonstrate a method f o r e x p l o r i n g l o w - c o n c e n t r a t i o n performance and t o i l l u s t r a t e the d a t a c h a r a c t e r i s t i c s t h a t such a method t y p i c a l l y r e v e a l s . A d a p t a t i o n s o f t h e method can be used by any l a b o r a t o r y f o r the e x p l o r a t o r y a n a l y s i s


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of chromatograms. There are, however, chromatograms that require some sophistication i n data analysis. Exploratory methods such as those discussed i n t h i s paper can be misleading. This paper does not discuss a l l the ways that the method might be misleading nor a l l the ways that the method might be improved. In the next section, some of the needed data analysis steps f o r the analysis of a single chromatogram are presented. In the t h i r d section, three properties of chromatograms, the pump cycle, the underlying white noise, and a low frequency component of unknown o r i g i n are discussed. In the fourth section, the question of how assessment of the detection l i m i t i s influenced by t h i s low frequency component and by the choice of peak i d e n t i f i c a t i o n and integration algorithm i s considered. I n i t i a l Processing of the Chromatogram The detection l i m i t f o r a p a r t i c u l a r analyte i s determined by the peak i n the chromatogram due to the analyte and by other variations that obscure t h i s peak. A chromatogram often has additional components that must be removed before the variations that determine the detection l i m i t can be analyzed. F i r s t , a chromatogram often has a water dip, some large peaks due to other analytes, and other gross v a r i a t i o n s . Second, a chromatogram often exhibits a slowly varying baseline. Third, a chromatogram from a system with a pump might exhibit a c y c l i c v a r i a t i o n due to the pump. In the chromatograms we consider, these components can e a s i l y be distinguished from the peak of interest. The water dip and large peaks due to other analytes do not coincide with the peak of interest; the baseline i s much smoother than the peak of interest; and the pump cycle repeats regularly i n time whereas the peak of interest does not. For these reasons, these components can be removed from the chromatogram with n e g l i g i b l e e f f e c t on the detection l i m i t . In other words, these components can be removed i n such a way that the r e s u l t i n g adjusted chromatogram can be analyzed as i f these components were never present. To i l l u s t r a t e the removal of these components, we consider a chromatogram that i s the r e s u l t of a sample consisting of 0.005 mg/L n i t r a t e and 0.025 mg/L s u l f a t e . The f i r s t 116 seconds of t h i s chromatogram consists of a short i n t e r v a l before sample i n j e c t i o n , the water dip, and a large peak immediately following the water dip due perhaps to a solvent inadvertently mixed with the sample. Since the variations i n the f i r s t 116 seconds are so large, we have excluded them from Figure 1 and from our analysis of t h i s chromatogram. Otherwise, Figure 1 shows the chromatogram as i t was produced by the instrument. As i n other figures i n t h i s paper, we r e t a i n the o r i g i n f o r the time scale that was set by the instrument. The most obvious feature i s the sulfate peak. What evidence there i s of n i t r a t e precedes the sulfate peak by about 120 seconds. To specify our estimates of the baseline and the pump cycle, we chromatogram as introduce some notation. delivered by the instrument. The conductance units are nS/cm. Let [tQ> tQ + Τ - 1] denote the i n t e r v a l selected f o r analysis. For t h i s chromatogram, we have tp = 117 and Τ = 799. S h i f t i n g the time o r i g i n to tQ - 1, we obtain y

(l)

( t )

=

Y

(0)

(

T

+

t

- i),

t

=

1,

..., Τ


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KOCH & LIGGETT

213

Critical Assessment of Detection Limits

In our estimation o f the baseline and pump cycle, we must exclude the sulfate peak. To specify the computations, we define a weight function w(t). This weight function includes the cosine-bell tapering of the ends of the intervals needed to reduce the bias i n spectral estimation (2). Let the i n t e r v a l to be excluded because i t has the sulfate peak be denoted by [ t , t ] . We l e t a


w(t) = = = = = =

(1 (1 (1 (1

-

0 cos(irt/21))/2 cos(TT(t-t )/21))/2 cos(-n(t-t )/21))/2 cosU(t-T-l)/21))/2 1 a

b

D

if t < t if 1 < t if 1 < t - t if 1 < t - t i f 1 < T-t+1 otherwise a

a

b

< < < <

Detection in Analytical Chemistry - American Chemical Society

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