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Development of a system for the detection of interferences during routine analysis by graphite furnace atomic absorption spectrometry
Chemometrics and intelligent laboratory systems Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
Development of a system for the detection of interferences during routine analysis by graphite furnace atomic absorption spectrometry W. Penninckx, J. Smeyers-Verbeke,
C. Hartmann, B. Bourguignon, D.L. Massart
Vrije Universiteit Brussel, Laarbeeklaan 103, 1090 Brussels, Belgium
(Received 9 August 1993; accepted 25 January 1994)
Abstract The development of a strategy for the detection of interferences during the routine analysis of unknown samples by graphite furnace atomic absorption spectrometry is discussed. Since indications of interferences must be found in the shape and position of the signal, different methods for the characterisation of the atomic absorption signal are evaluated. For each signal different correlated parameters are monitored, so that the possibility to summarise them in a multivariate test statistic, called Hotelling’s T’, is investigated. The use of control limits for this parameter, established from the measurement results in matrix-free solutions, permits the detection of interferences. However, it is much more difficult to say how strongly the quality of the determination is affected by the detected interferences. Another problem that remains to be solved is the fact that it is difficult to compare signals that are measured in different runs.
1. Introduction The use of analytical data is strongly dependent on their reliability. Therefore it is necessary to demonstrate the ability of a method to produce correct results, prior to its application in routine analysis. The strategy that is used in this validation process is often dependent on the measurement technique (high-performance liquid chromatography, graphite furnace atomic absorption spectrometry, etc.) since specific problems must be traced. In atomic absorption spectrometry, matrix interferences are considered as the main source of error. Generally a calibration line prepared in matrix-free solutions is used to estimate the analyte concentration from the ab0169-7439/94/$07.00
sorbances measured in the unknown samples, so that it is essential to prove that the sample matrix does not affect the determination of the analyte in an important way. To accomplish this, the slopes of a standard addition and an aqueous calibration line are compared. Interferences are reflected in a difference in slope. Since the composition of each sample is unique and can affect the determination in its own way, theoretically, this investigation should be performed for each sample in which the analyte concentration must be determined. However, in practice this is not possible. Therefore, during the validation of the method, interferences are traced in a small number of samples which are assumed to be representative for a larger population. When, for example,
0 1994 Elsevier Science B.V. All rights reserved
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138
W. Penninchx et al. / Chemometrics
and Intelligent Laboratory
a method is developed for the analysis of blood, two or three samples are examined, and a conclusion is drawn for all blood samples, based on these results. Although this seems an acceptable strategy, important differences can occur in the matrix composition of some sample types. Urine samples, for example, can contain various amounts of highly interfering inorganic salts [l]. Consequently, it is possible that samples which are routinely analysed contain larger amounts of interfering salts than the samples which were used for the validation of the analysis method. Moreover, in many cases the analyst has little information on the composition of the sample and the variations that can occur. Suppose for example that a method for the determination of Cu in cheese is applied for the analysis of many types of cheese. In practice the method will be validated for a number of cheeses which are supposed to contain the largest amounts of interfering compounds (fat, salts, etc.). It is however possible that the composition of one of the samples is such that an unexpected matrix interference occurs. It is clear that there is a certain need to trace unexpected interferences that occur during the routine analysis of unknown samples. Since the analyte concentration in the samples is unknown, no information can be found in the peak area. Thus, indications of interferences must be traced in the shape and position of the signal. In practice, the signal measured in the sample solution should be compared with a reference signal, measured in a matrix-free solution. The signals that are measured in aqueous solutions for calibration purposes can be used as references. The first step in the development of a system for the tracing of unforeseen interferences during routine analysis of unknown samples is the selection of appropriate parameters for the characterisation of the atomic absorbance signal. These parameters should be strongly affected by changes in the signal caused by interferents but, on the other hand, they should be independent of the analyte concentration. Since the analyte concentration in the sample is unknown, it must be possible to compare the obtained signal with a reference signal that corresponds with another
Systems 23 (1994) 137-148
concentration. In the past, atomic absorbance signals have been characterised in a number of different ways [2-41. To evaluate the effect of interferents on the graphite furnace signal, Harnly [3] measured the time intervals between the start of the atomisation cycle and a number of critical peak parameters, such as the time of the appearance of the signal and of the peak maximum. The use of the formulas of the statistical moments was proposed by Wegscheider et al. [4]. The applicability of these two strategies, and a third alternative based on the linearisation of parts of the signal, is examined for the characterisation of the lead signal. Lead is selected since it is known to be a volatile element, of which the determination is strongly affected by interferences [5]. The effect of the presence of two important sources of interferences, namely sodium chloride and potassium sulphate [l], on the shape of the signal is investigated. A decreasing sensitivity in the presence of increasing amounts of these salts was demonstrated. An aqueous solution containing a single interfering component, of course, cannot be considered as a placebo of a real sample, which may contain a mixture of different interferents. However, this way of working permits to investigate whether it is worthwhile to proceed in this way. If small amounts of a single interferent can be traced it must also be possible to trace mixtures of larger amounts of interferents. After the selection of appropriate parameters, control limits must be established. Therefore one must estimate the variation that can be expected on the monitored parameter when the measurement process is ‘under control’. This variation is then the result of the pure error in the measurement. Since the aim of this work is to trace matrix interferences, measurements that are performed in a matrix-free environment (i.e., in aqueous solutions) must be considered to be ‘under control’. Consequently, control limits for the monitored parameter are established by performing replicate measurements in aqueous solutions. When in a sample solution a signal is measured for which the parameter has an unexpected value (outside the control limits), one can conclude that the signal does not behave as in a matrix-free solution, thus that the matrix affects the determi-
W. Penninckv et al. / Chemometrics and Intelligent Laboratory Systems 23 (I 994) 137-148
nation. In such a situation there exists also a potential effect on the sensitivity. The parameters which characterise the signal can be monitored individually. However, when for each measurement result different correlated parameters are monitored, the use of univariate control limits may cause severe problems [6]. For a situation of two correlated variables, for example, misleading conclusions will be obtained since the control region is considered rectangular while the true region is elliptical. Moreover, when many parameters are used simultaneously for the same measurement, the (Y error rate will increase. For non-correlated variables this effect can be reduced by using m/p instead of CYfor each individual parameter, where p represents the number of variables. Finally, when results for many variables are produced simultaneously, the evaluation of all individual results may become labori-
139
ous. These problems may be solved by the use of a multivariate parameter, which summarises the information given by the univariate parameters. In this work the applicability of Hotelling’s T* statistic [6] is examined. However, it is not only important to trace interferences, but also to investigate how strongly they affect the sensitivity. Stated otherwise: do they affect the quality of the measurements in a more important way than foreseen during the method validation. Consequently, apart from control limits, tolerance limits should be developed. Therefore it is important to examine whether a correlation exists between the strength of the interferences and the monitored parameter. If we consider the example of the urine analysis, we can assume that the interfering effect of the matrix is determined by the concentration of a number of salts. Thus, increasing salt concentra-
absorbance
Fig. 1. The time intervals between the start of the atomisation cycle and (a) the moment that l/e* of the peak maximum is reached, (b) the moment that l/e of the peak maximum is reached, Cc) the moment that l/2 of the peak maximum is reached, (d) the peak maximum, (e) the decay to l/2 of the peak maximum, (f) the decay to l/e of the peak maximum, (g) the decay to l/e* of the peak maximum. From these parameters the peak width at l/2, l/e and l/e* of the peak height can be calculated (wJ., wt, and W, respectively). The time intervals between the start of the atomisation cycle and (h) the inflection point in the atomisation part of the signal and (8 the inflection point in the diffusion part of the signal are not shown.
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tions should result in increasing T2 value. In practice this was tested by determining lead in the presence of increasing amounts of NaCl and K,SO,.
2. Experimental 2.1. Collecting and handling of the data
All lead determinations are performed on a Perkin-Elmer Zeeman 3030 atomic absorption spectrometer, using a single pyrolytic coated tube with platform. The injection volume was 10 ~1 and 6 pg Pd + 15 pg Mg(NO,), is added as chemical modifier [ll. A pyrolysis temperature of 1200” C was applied. First aqueous standard solutions containing 20 pg/l, 40 pg/l, 60 pg/l, 80 pg/l and 100 pg/l lead were measured. Then 100 pug/l Pb solutions in the presence of O.O%, 0.5%, 1.0% or 1.5% NaCl were analysed for the evaluation of the effect of sodium chloride. Finally solutions containing 100 pg/l Pb were analysed in O.O%, O.l%, 0.2% or 0.3% K,SO,. The digitised signals (50 data per second) are recorded by the spectrometer’s RS-232 interface [7], and each signal is written to a separate file by a Quick-Basic programme. The peak parameters and the test statistics for the control charts are calculated by programmes written in Visual Basic. Sirius [8] was used to perform the principal component analysis. 2.2. Characterisation of the signal In this work easily computable and generally applicable signal parameters are looked for. Due to their simplicity it is often difficult to explain the chemical meaning of a change in these parameters. However, our aim is just to trace unexpected interferences, and not to examine how the different processes that determine the shape of the atomic absorption signal are affected, which would require a more complete description of the signal. Although the shape of the signal is determined by a number of different processes, for reasons of simplicity, the part of the signal before
Systems 23 (1994) 137-148
and after the peak maximum are referred to as the atomisation and diffusion part, respectively. The first way of signal characterisation is based on the measurement of the time of a number of critical peak parameters. Other workers [2,3] computed the time interval between the start of the atomisation cycle and the appearance of the signal, the peak maximum, the decay to l/2 of the peak maximum, the decay to l/e of the peak maximum, the decay to l/e2 of the peak maximum and the end of the absorbance signal (Fig. 1). Since these parameters mainly describe the diffusion part of the signal and give little information about the atomisation part, we also calculate the intervals between the start of the atomisation cycle and the moment that l/e2, l/e and l/2 of the peak maximum is reached. From parameters, the width of the signal can be calculated at the different heights. Additionally, the time intervals between the start of the atomisation cycle and inflection points in the signal are calculated. To accomplish this the first derivative of a nine-point moving average filtered signal is calculated. This first derivative is also filtered before the second derivative is computed. Wegscheider et al. [4] used the statistical moments to describe the atomic absorption signal. Table 1 summarises how these statistics can be calculated 191. The first moment cm,> characterises the position of the signal while the second moment is a measure of the lateral spreading. The asymmetry and flatness of the signal are described by the third cm,> and fourth cm,> moment, respectively. From these, two dimensionless parameters can be calculated named skew and kurtosis.
Table 1 The calculation
of the statistical
moments
Eti.Ai
C( t, - m,)’ m2=
ml=m3=
a
E(tl - m,)3’Ai
C(ti - m,)‘.A, m4=
EAi
LA, skew = -
m3 3/2
kurtosis
= 2
m2
a Ai is the absorbance
.A,
LA;
m22
measured
at time
tj.
- 3
W. Penninckx et al. / Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
2.3. Control limits
A third way for the characterisation of the signal is based on the linearisation of parts of the signal after a logarithmic transformation. Changes in the slope of these linear parts can then be monitored. Since the part of the signal before and after the peak maximum both seem to have a sigmoid form, we also investigated whether it is possible to linearise them by the application of a logistic transformation [lo]:
Control limits must be established to trace changes in the parameters that describe the shape and position of the signal. All limits in this work are calculated with a confidence level of 5%. The applied multivariate test statistic, called Hotelling’s T*, is based on the multivariate normal distribution and is calculated as: T* = (x,,, -Zc)‘S-l(x,
logit( Ai) = In & i
141
-Xc)
(2)
where x, is the vector representing multivariate result for the monitored sample, X, is the vector
II
* 0 c3
1.80
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m \
o
1
I’.
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r
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I
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I 0.0
I
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/
OoO 1
J
I
--
\
/
--U.-ii/
A’
0.1“
--0.0
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<07.8X)
Fig. 2. PC1 versus PC2 biplot, derived from the time parameters, obtained from the measurement of lead standard solutions containing different K,SO, concentrations (0.0, 0.1, 0.2 and 0.3%). The objects are represented as the K,SO, concentrations (in percent). The variable names are encircled and explained in Fig. 1.
142
W Penninckx et al. / Chernometrics and Intelligent Laboratory
representing the means of the replicate measurement results of the reference solution and S is an estimate of the variance-covariance matrix. Generally no tables are provided for the T2 distribution since it is related to the F distribution by the relationship [6]: T2 = P(n - 1) (3)
Fp,n-_p
P.n n-p
where p represents
the number of variables and
4.50
Systems 23 (1994) 137-148
n the number of replicate measurements of the control sample. Since the test statistic has a quadratic form, only the upper control limit is used. The interpretation of an out of control situation can be difficult. Therefore it is sometimes recommended to use the T2 chart together with individual x charts with control limits based on (Y/P. The fact that the number of replicate measurements of the control sample must exceed the number of control variables substantially is another disadvantage of T2 charts.
0
rcra
a.00
G 6 . I: u
--
---
1.50
I 23
(Y
6
- -g\/
72
/ /
5 sp
/
1 ,' 0.00
af ‘63
/
\/
/ <5
/
0p
,'P
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I I
14, 182
b'
11
.
' e 8-
-e
A-
-1.50
-3.40
-1.70
-0.00 Conponant
1.70 1
3.40
5.10
<80.7X)
Fig. 3. PC1 versus PC2 biplot, derived from the time interval parameters and the peak area, obtained from the measurement of matrix-free lead standard solutions at different stages of the lifetime of the tube. The signals are numbered corresponding to the sequence they were recorded. The variable names are encircled and explained in Fig. 1.
W Penninckr et al. / Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
3. Results 3.1. Characterisation of the signal In order to visualise the effect of the analyte concentration and the presence of interferents, a principal component analysis is performed on the experimental results. All data are standardised and centred prior to the analysis. The results are presented as biplots [S]. 3.1.1. Time of critical peak parameters Fig. 2 shows the PC1 versus PC2 biplot, which is derived from the parameters obtained from the measurement of standard solutions containing different K,SO, concentrations. Along PCl, which explains almost 90% of the variation, a distinction can be made between signals that are measured in the presence of different concentrations of the interfering salt. Potassium sulphate clearly induces an acceleration of the appearance of the signal, which is reflected in a decrease of all time parameters. PC2 contains no information on the interferent concentration. A principal component analysis that was performed on the lead signals measured in solutions containing different amount of sodium chloride (not shown
143
here), indicated that this salt delays the appearance of the lead signal, which is reflected in an increase of the time parameters. For this salt, the measurement results obtained in the presence of different interferent concentrations form no clear clusters. Monitoring of the peak width gives no additional information. However, it was also observed that the shape and position of the atomic absorption signal, measured in a matrix-free environment, changes during the lifetime of the tube. Consequently, to trace interferences, the signal measured in the sample solution should be compared with a reference signal that is measured at the same stage of the lifetime of the tube. Moreover, no clear correlation can be found between the change of the shape of the signal and the ageing of the tube or the loss of sensitivity, which hampers a simple standardisation. This is illustrated in Fig. 3 where the PC1 versus PC2 biplot is shown. The variables in this plot are the signal parameters, measured in matrix-free solutions, during the complete lifetime of the tube. The objects correspond to the stage of the lifetime of the tube at which the signal was obtained. PCl, which explains 80.7% of the variance, is mainly determined by the parameters describing the peak shape and
(4
(b)
Fig. 4. The effect of the broadening of the diffusion stage of the signal on the critical peak parameters (At) and on the absorbance measured at a certain time (AA), for (a) a sharp signal and (b) a signal with strong tailing.
W. Penninckx et al. /Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
144
position. PC2, which is correlated with the age of the graphite tube, is mainly determined by the peak area. 3.1.2. Statistical moments The statistical moments seem less suitable for the characterisation of the lead signal since they are dependent on the analyte concentration. The second moment is found to be strongly affected by the lead concentration but little by the interferents concentration. The signal becomes sharper for increasing lead concentrations. For the fourth moment, on the other hand, this is just the opposite. The first and third moments are affected by both factors. The fact that the statistical moments are dependent on the concentration while this is not the case for the time intervals can probably be explained by the shape of the signal. The lead signal consists of a strongly ascending atomisation part and a strongly descending diffusion part. As is illustrated in Fig. 4, in such a situation a small
broadening of the signal has little effect on the time intervals (At), but an important difference in the absorbance that is measured at each moment can be observed (AA), which is reflected in the second moment. 3.1.3. The slope of linear parts after linearisation
The concentration effect was eliminated by dividing the individual absorbances that constitute a signal by their maximal value. No reproducible linear parts can be found in the lead signal after a logarithmic transformation (In Ai). When a \Itransformation was applied, an important linear part can be distinguished in the atomisation part of the signal, while a small linear part can be found just after the maximum (see Fig. 5). The second derivative of the signal can be used to determine these linear parts. An important linear part at the end of the signal is found after a logistic transformation (Eq. 1). The speed of the appearance of the signal is significantly accelerated in the presence of K,SO, and
time
-I &&Aj))
I Fig. 5. Pure lead signal after a dq
transformation
together
with the second derivative of the signal.
W. Penninckx et al. /Chemometrics
and Intelligent Laboratory
Systems 23 (1994) 137-148
145
(a) .
350
300
250
. P
200
1,
150
f
. .
100
50
0
_--___--~--__-~-----~~~---~~-~~~~~~~~~~-------------------t
UCL
I
I
t
I
1 1
0.2
0.1
0
L I
03
Potassium sulphate concentration (%)
180
.
03
180
140
.
120
loo P 80
00
40
0
f 0
1
I
0.5
1
I
1.5
Sodium chloride concentration (%) Fig. 6. T2 value for signals measured in (a) different potassium sulphate concentrations and (b) different sodium chloride concentrations, calculated from the time intervals between the start of the atomisation cycle and the moment that l/e2 of the peak maximum is reached, the peak maximum and the decay to l/e2 of the peak maximum, together with the upper control limit.
146
W. Penninckx et al. /Chemometrics
and Intelligent Laboratory
Systems 23 (1994) 137-148
. (a)
* 1.5
.
t . f _--_----__---__----_--
;-----
. ----------------------------_--
.
&
: Ba 1
.
1
2
Potassium sulphate concentration (%)
0
.
-0.5
-1
t -1.5
r
__-_____-________--___--__--~____-___-_____-_________-___ __----
Bd
i _-__-_-___-____--_---~-__--__---____-____-~--
___-_
-2
-2.5
. &
-3 i
:
-3.5
Potassium sulphate concentration (%) Fig. 7. Slope of the Iinearised part in the atomisation different potassium chloride concentrations, together
stage of the signal (B,) and the diffusion stage (B,) of the signal measured with the upper and lower control limits (positioned at 3~).
in
W. Permit&x
et al. /Chemometrics
and Intelligent Laboratory
Systems 23 (1994) 137-148
slightly slowed down in the presence of NaCl. The speed of the diffusion is decreased by NaCl and hardly influenced by K,SO,.
mainly affects the atomisation diffusion stage of the signal.
3.2. Establishment of the control limits
4. Conclusions
Matrix-free reference solutions and monitored samples are measured in the same run, because as explained earlier the shape and position of the signals change during the lifetime of the tube. Since the use of Hotelling’s T2 requires that the number of replicate measurements of the reference solution substantially exceeds the number of control variables, only three variables were monitored: one in the atomisation stage, the peak maximum and one in the diffusion stage. Fig. 6 shows, for Pb in the presence of K,SO, or NaCl, the T2 values which are computed from the time intervals between the start and the atomisation cycle and (a> the moment that l/e* of the peak maximum is reached, (b) the peak maximum is reached and cc> the decay to l/e2 of the maximum, together with the upper control limits. All signals which are measured in the presence of K,SO, result in a T2 value above the upper control limit (Fig. 6a). Moreover a correlation can be seen between the K,SO, concentration and the T2 value. Although in all NaCl containing solutions signals were measured which are significantly different from the reference, no correlation can be observed between the NaCl concentration and the T2 value (Fig. 6b), which hampers the possible use of the T2 value to evaluate the effect of interferences on the quality of the determination. When the individual parameters are monitored, similar information is obtained. However, for some of the sodium chloride containing solutions, no abnormal values are found for the parameter related to the atomisation stage. Similar results are obtained when other time parameters were monitored. The investigated interferences are not reflected in the peak width. Monitoring the slope of the linearised part in the diffusion stage clearly permits the tracing of potassium sulphate interferences (Fig. 7b). The effect of K,SO, on the atomisation is less clear (Fig. 7a). Sodium chloride, on the other hand,
147
stage and not the
Interferences can be traced by comparing the lead signal with a reference signal, measured in a matrix-free environment. This was demonstrated for two important interfering salts. It is not clear if this can be generalised for other types of interferences. Good results are obtained when the different signal parameters are summarised in a Hotelling’s T2 value. For the moment we are investigating if this finding is confirmed for two other elements, namely aluminium, a less volatile element with different characteristics, and copper. One of the main problems is the changing of the shape of the signal during the lifetime of the tube, so that the monitored sample should be measured in the same run as the matrix-free reference. Moreover, the number of replicate measurements of the reference solution should substantially exceed the number of variables. Therefore it will be investigated if it is possible to standardise the signals that are measured at different stages of the lifetime of the tube, or even in different tubes of the same type, so that they can be compared. Until now control limits were used, which indicate that the measurement conditions are different from those in a matrix-free environment. In a further stage acceptance limits should be developed, which indicate up to which level acceptable interferences occur.
References [ll W. Penninckx, D.L. Massart and J. Smeyers-Verbeke, Effectiveness of palladium as a chemical modifier for the determination of lead in biological materials and foodstuffs by graphite furnace atomic absorption spectrometry, Fresenius' Journal of Analytical Chemistry, 343 (1992) 526-531. 121 W.B. Barnett and M.C. Cooksey, A study of graphite furnace peak shapes with a computer, Atomic Absorption Newsletter, 18 (1979) 61-64. [3] J.M. Harnly, Evaluation of graphite furnace atomic ab-
148
W. Penninckx et al. /Chemometrics
and Intelligent Laboratory
sorption signals using the peak shape and position, Journal of Analytical Atomic
Spectrometry,
3 (1988) 43-51.
[4] W. Wegscheider,
L. Jan%, M.T. Phe and M.R.A. Michaelis, Sensitivity estimation by the analysis of peak shapes in graphite furnace atomic absorption spectrometry, Chemometrics and Intelligent Laboratory Systems, I
(1990) 281-293. 151 G. Schlemmer and B. Welz, Palladium and magnesium
nitrates, a more universal modifier for graphite furnace atomic absorption spectrometry, Spectrochimica Acta, 41B (1986) 1157-1165. 161 J.E. Jackson, A User’s Guide to Principal
Wiley, New York, pp. 19-25.
Components,
Systems 23 (1994) 137-148
171 W.B. Barnett, W. Bohler, G.R. Canrick and W. Slavin,
Signal processing and detection limits for graphite furnace atomic absorption with Zeeman background correction, Spectrochimica Acta, 40B (1985) 1689-1703. [8] T.V. Karstang and O.M. Kvalheim, Sirius, a Program for Multivariate Calibration and Classification, University of Bergen, Bergen, 1990. [9] N. Dyson, Chromatographic Integration Methods, Royal Society of Chemistry, Loughborough, 1990, pp. 20-23. [lo] D.G. Kleinbaum, L.L. Kupper and H. Morgenstern, Epidemiologic Research, Van Nostrand Reinhold, New York, 1982, pp. 421-423.
Development of a system for the detection of interferences during routine analysis by graphite furnace atomic absorption spectrometry W. Penninckx, J. Smeyers-Verbeke,
C. Hartmann, B. Bourguignon, D.L. Massart
Vrije Universiteit Brussel, Laarbeeklaan 103, 1090 Brussels, Belgium
(Received 9 August 1993; accepted 25 January 1994)
Abstract The development of a strategy for the detection of interferences during the routine analysis of unknown samples by graphite furnace atomic absorption spectrometry is discussed. Since indications of interferences must be found in the shape and position of the signal, different methods for the characterisation of the atomic absorption signal are evaluated. For each signal different correlated parameters are monitored, so that the possibility to summarise them in a multivariate test statistic, called Hotelling’s T’, is investigated. The use of control limits for this parameter, established from the measurement results in matrix-free solutions, permits the detection of interferences. However, it is much more difficult to say how strongly the quality of the determination is affected by the detected interferences. Another problem that remains to be solved is the fact that it is difficult to compare signals that are measured in different runs.
1. Introduction The use of analytical data is strongly dependent on their reliability. Therefore it is necessary to demonstrate the ability of a method to produce correct results, prior to its application in routine analysis. The strategy that is used in this validation process is often dependent on the measurement technique (high-performance liquid chromatography, graphite furnace atomic absorption spectrometry, etc.) since specific problems must be traced. In atomic absorption spectrometry, matrix interferences are considered as the main source of error. Generally a calibration line prepared in matrix-free solutions is used to estimate the analyte concentration from the ab0169-7439/94/$07.00
sorbances measured in the unknown samples, so that it is essential to prove that the sample matrix does not affect the determination of the analyte in an important way. To accomplish this, the slopes of a standard addition and an aqueous calibration line are compared. Interferences are reflected in a difference in slope. Since the composition of each sample is unique and can affect the determination in its own way, theoretically, this investigation should be performed for each sample in which the analyte concentration must be determined. However, in practice this is not possible. Therefore, during the validation of the method, interferences are traced in a small number of samples which are assumed to be representative for a larger population. When, for example,
0 1994 Elsevier Science B.V. All rights reserved
SSDI 0169-7439(94)00008-7
138
W. Penninchx et al. / Chemometrics
and Intelligent Laboratory
a method is developed for the analysis of blood, two or three samples are examined, and a conclusion is drawn for all blood samples, based on these results. Although this seems an acceptable strategy, important differences can occur in the matrix composition of some sample types. Urine samples, for example, can contain various amounts of highly interfering inorganic salts [l]. Consequently, it is possible that samples which are routinely analysed contain larger amounts of interfering salts than the samples which were used for the validation of the analysis method. Moreover, in many cases the analyst has little information on the composition of the sample and the variations that can occur. Suppose for example that a method for the determination of Cu in cheese is applied for the analysis of many types of cheese. In practice the method will be validated for a number of cheeses which are supposed to contain the largest amounts of interfering compounds (fat, salts, etc.). It is however possible that the composition of one of the samples is such that an unexpected matrix interference occurs. It is clear that there is a certain need to trace unexpected interferences that occur during the routine analysis of unknown samples. Since the analyte concentration in the samples is unknown, no information can be found in the peak area. Thus, indications of interferences must be traced in the shape and position of the signal. In practice, the signal measured in the sample solution should be compared with a reference signal, measured in a matrix-free solution. The signals that are measured in aqueous solutions for calibration purposes can be used as references. The first step in the development of a system for the tracing of unforeseen interferences during routine analysis of unknown samples is the selection of appropriate parameters for the characterisation of the atomic absorbance signal. These parameters should be strongly affected by changes in the signal caused by interferents but, on the other hand, they should be independent of the analyte concentration. Since the analyte concentration in the sample is unknown, it must be possible to compare the obtained signal with a reference signal that corresponds with another
Systems 23 (1994) 137-148
concentration. In the past, atomic absorbance signals have been characterised in a number of different ways [2-41. To evaluate the effect of interferents on the graphite furnace signal, Harnly [3] measured the time intervals between the start of the atomisation cycle and a number of critical peak parameters, such as the time of the appearance of the signal and of the peak maximum. The use of the formulas of the statistical moments was proposed by Wegscheider et al. [4]. The applicability of these two strategies, and a third alternative based on the linearisation of parts of the signal, is examined for the characterisation of the lead signal. Lead is selected since it is known to be a volatile element, of which the determination is strongly affected by interferences [5]. The effect of the presence of two important sources of interferences, namely sodium chloride and potassium sulphate [l], on the shape of the signal is investigated. A decreasing sensitivity in the presence of increasing amounts of these salts was demonstrated. An aqueous solution containing a single interfering component, of course, cannot be considered as a placebo of a real sample, which may contain a mixture of different interferents. However, this way of working permits to investigate whether it is worthwhile to proceed in this way. If small amounts of a single interferent can be traced it must also be possible to trace mixtures of larger amounts of interferents. After the selection of appropriate parameters, control limits must be established. Therefore one must estimate the variation that can be expected on the monitored parameter when the measurement process is ‘under control’. This variation is then the result of the pure error in the measurement. Since the aim of this work is to trace matrix interferences, measurements that are performed in a matrix-free environment (i.e., in aqueous solutions) must be considered to be ‘under control’. Consequently, control limits for the monitored parameter are established by performing replicate measurements in aqueous solutions. When in a sample solution a signal is measured for which the parameter has an unexpected value (outside the control limits), one can conclude that the signal does not behave as in a matrix-free solution, thus that the matrix affects the determi-
W. Penninckv et al. / Chemometrics and Intelligent Laboratory Systems 23 (I 994) 137-148
nation. In such a situation there exists also a potential effect on the sensitivity. The parameters which characterise the signal can be monitored individually. However, when for each measurement result different correlated parameters are monitored, the use of univariate control limits may cause severe problems [6]. For a situation of two correlated variables, for example, misleading conclusions will be obtained since the control region is considered rectangular while the true region is elliptical. Moreover, when many parameters are used simultaneously for the same measurement, the (Y error rate will increase. For non-correlated variables this effect can be reduced by using m/p instead of CYfor each individual parameter, where p represents the number of variables. Finally, when results for many variables are produced simultaneously, the evaluation of all individual results may become labori-
139
ous. These problems may be solved by the use of a multivariate parameter, which summarises the information given by the univariate parameters. In this work the applicability of Hotelling’s T* statistic [6] is examined. However, it is not only important to trace interferences, but also to investigate how strongly they affect the sensitivity. Stated otherwise: do they affect the quality of the measurements in a more important way than foreseen during the method validation. Consequently, apart from control limits, tolerance limits should be developed. Therefore it is important to examine whether a correlation exists between the strength of the interferences and the monitored parameter. If we consider the example of the urine analysis, we can assume that the interfering effect of the matrix is determined by the concentration of a number of salts. Thus, increasing salt concentra-
absorbance
Fig. 1. The time intervals between the start of the atomisation cycle and (a) the moment that l/e* of the peak maximum is reached, (b) the moment that l/e of the peak maximum is reached, Cc) the moment that l/2 of the peak maximum is reached, (d) the peak maximum, (e) the decay to l/2 of the peak maximum, (f) the decay to l/e of the peak maximum, (g) the decay to l/e* of the peak maximum. From these parameters the peak width at l/2, l/e and l/e* of the peak height can be calculated (wJ., wt, and W, respectively). The time intervals between the start of the atomisation cycle and (h) the inflection point in the atomisation part of the signal and (8 the inflection point in the diffusion part of the signal are not shown.
140
W Penninckx et al. / Chemometrics
and Intelligent Laboratory
tions should result in increasing T2 value. In practice this was tested by determining lead in the presence of increasing amounts of NaCl and K,SO,.
2. Experimental 2.1. Collecting and handling of the data
All lead determinations are performed on a Perkin-Elmer Zeeman 3030 atomic absorption spectrometer, using a single pyrolytic coated tube with platform. The injection volume was 10 ~1 and 6 pg Pd + 15 pg Mg(NO,), is added as chemical modifier [ll. A pyrolysis temperature of 1200” C was applied. First aqueous standard solutions containing 20 pg/l, 40 pg/l, 60 pg/l, 80 pg/l and 100 pg/l lead were measured. Then 100 pug/l Pb solutions in the presence of O.O%, 0.5%, 1.0% or 1.5% NaCl were analysed for the evaluation of the effect of sodium chloride. Finally solutions containing 100 pg/l Pb were analysed in O.O%, O.l%, 0.2% or 0.3% K,SO,. The digitised signals (50 data per second) are recorded by the spectrometer’s RS-232 interface [7], and each signal is written to a separate file by a Quick-Basic programme. The peak parameters and the test statistics for the control charts are calculated by programmes written in Visual Basic. Sirius [8] was used to perform the principal component analysis. 2.2. Characterisation of the signal In this work easily computable and generally applicable signal parameters are looked for. Due to their simplicity it is often difficult to explain the chemical meaning of a change in these parameters. However, our aim is just to trace unexpected interferences, and not to examine how the different processes that determine the shape of the atomic absorption signal are affected, which would require a more complete description of the signal. Although the shape of the signal is determined by a number of different processes, for reasons of simplicity, the part of the signal before
Systems 23 (1994) 137-148
and after the peak maximum are referred to as the atomisation and diffusion part, respectively. The first way of signal characterisation is based on the measurement of the time of a number of critical peak parameters. Other workers [2,3] computed the time interval between the start of the atomisation cycle and the appearance of the signal, the peak maximum, the decay to l/2 of the peak maximum, the decay to l/e of the peak maximum, the decay to l/e2 of the peak maximum and the end of the absorbance signal (Fig. 1). Since these parameters mainly describe the diffusion part of the signal and give little information about the atomisation part, we also calculate the intervals between the start of the atomisation cycle and the moment that l/e2, l/e and l/2 of the peak maximum is reached. From parameters, the width of the signal can be calculated at the different heights. Additionally, the time intervals between the start of the atomisation cycle and inflection points in the signal are calculated. To accomplish this the first derivative of a nine-point moving average filtered signal is calculated. This first derivative is also filtered before the second derivative is computed. Wegscheider et al. [4] used the statistical moments to describe the atomic absorption signal. Table 1 summarises how these statistics can be calculated 191. The first moment cm,> characterises the position of the signal while the second moment is a measure of the lateral spreading. The asymmetry and flatness of the signal are described by the third cm,> and fourth cm,> moment, respectively. From these, two dimensionless parameters can be calculated named skew and kurtosis.
Table 1 The calculation
of the statistical
moments
Eti.Ai
C( t, - m,)’ m2=
ml=m3=
a
E(tl - m,)3’Ai
C(ti - m,)‘.A, m4=
EAi
LA, skew = -
m3 3/2
kurtosis
= 2
m2
a Ai is the absorbance
.A,
LA;
m22
measured
at time
tj.
- 3
W. Penninckx et al. / Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
2.3. Control limits
A third way for the characterisation of the signal is based on the linearisation of parts of the signal after a logarithmic transformation. Changes in the slope of these linear parts can then be monitored. Since the part of the signal before and after the peak maximum both seem to have a sigmoid form, we also investigated whether it is possible to linearise them by the application of a logistic transformation [lo]:
Control limits must be established to trace changes in the parameters that describe the shape and position of the signal. All limits in this work are calculated with a confidence level of 5%. The applied multivariate test statistic, called Hotelling’s T*, is based on the multivariate normal distribution and is calculated as: T* = (x,,, -Zc)‘S-l(x,
logit( Ai) = In & i
141
-Xc)
(2)
where x, is the vector representing multivariate result for the monitored sample, X, is the vector
II
* 0 c3
1.80
“ 1I \ow
m \
o
1
I’.
/O-8.0 @
/
O-;).2,+ .
/
/
/
0.3
\
\
I
0.3
\
J
-2.60
I
d
*&I @ \ h,i Smo I I I
r
\
-5.20
0.00 componsnt
2.60 1
I
0
\
0.2 I \_t53
2. -
I 0.0
I
0.2
I
Q&I
I
/
OoO 1
J
I
--
\
/
--U.-ii/
A’
0.1“
--0.0
5.20
<07.8X)
Fig. 2. PC1 versus PC2 biplot, derived from the time parameters, obtained from the measurement of lead standard solutions containing different K,SO, concentrations (0.0, 0.1, 0.2 and 0.3%). The objects are represented as the K,SO, concentrations (in percent). The variable names are encircled and explained in Fig. 1.
142
W Penninckx et al. / Chernometrics and Intelligent Laboratory
representing the means of the replicate measurement results of the reference solution and S is an estimate of the variance-covariance matrix. Generally no tables are provided for the T2 distribution since it is related to the F distribution by the relationship [6]: T2 = P(n - 1) (3)
Fp,n-_p
P.n n-p
where p represents
the number of variables and
4.50
Systems 23 (1994) 137-148
n the number of replicate measurements of the control sample. Since the test statistic has a quadratic form, only the upper control limit is used. The interpretation of an out of control situation can be difficult. Therefore it is sometimes recommended to use the T2 chart together with individual x charts with control limits based on (Y/P. The fact that the number of replicate measurements of the control sample must exceed the number of control variables substantially is another disadvantage of T2 charts.
0
rcra
a.00
G 6 . I: u
--
---
1.50
I 23
(Y
6
- -g\/
72
/ /
5 sp
/
1 ,' 0.00
af ‘63
/
\/
/ <5
/
0p
,'P
-b,c
I I
14, 182
b'
11
.
' e 8-
-e
A-
-1.50
-3.40
-1.70
-0.00 Conponant
1.70 1
3.40
5.10
<80.7X)
Fig. 3. PC1 versus PC2 biplot, derived from the time interval parameters and the peak area, obtained from the measurement of matrix-free lead standard solutions at different stages of the lifetime of the tube. The signals are numbered corresponding to the sequence they were recorded. The variable names are encircled and explained in Fig. 1.
W Penninckr et al. / Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
3. Results 3.1. Characterisation of the signal In order to visualise the effect of the analyte concentration and the presence of interferents, a principal component analysis is performed on the experimental results. All data are standardised and centred prior to the analysis. The results are presented as biplots [S]. 3.1.1. Time of critical peak parameters Fig. 2 shows the PC1 versus PC2 biplot, which is derived from the parameters obtained from the measurement of standard solutions containing different K,SO, concentrations. Along PCl, which explains almost 90% of the variation, a distinction can be made between signals that are measured in the presence of different concentrations of the interfering salt. Potassium sulphate clearly induces an acceleration of the appearance of the signal, which is reflected in a decrease of all time parameters. PC2 contains no information on the interferent concentration. A principal component analysis that was performed on the lead signals measured in solutions containing different amount of sodium chloride (not shown
143
here), indicated that this salt delays the appearance of the lead signal, which is reflected in an increase of the time parameters. For this salt, the measurement results obtained in the presence of different interferent concentrations form no clear clusters. Monitoring of the peak width gives no additional information. However, it was also observed that the shape and position of the atomic absorption signal, measured in a matrix-free environment, changes during the lifetime of the tube. Consequently, to trace interferences, the signal measured in the sample solution should be compared with a reference signal that is measured at the same stage of the lifetime of the tube. Moreover, no clear correlation can be found between the change of the shape of the signal and the ageing of the tube or the loss of sensitivity, which hampers a simple standardisation. This is illustrated in Fig. 3 where the PC1 versus PC2 biplot is shown. The variables in this plot are the signal parameters, measured in matrix-free solutions, during the complete lifetime of the tube. The objects correspond to the stage of the lifetime of the tube at which the signal was obtained. PCl, which explains 80.7% of the variance, is mainly determined by the parameters describing the peak shape and
(4
(b)
Fig. 4. The effect of the broadening of the diffusion stage of the signal on the critical peak parameters (At) and on the absorbance measured at a certain time (AA), for (a) a sharp signal and (b) a signal with strong tailing.
W. Penninckx et al. /Chemometrics and Intelligent Laboratory Systems 23 (1994) 137-148
144
position. PC2, which is correlated with the age of the graphite tube, is mainly determined by the peak area. 3.1.2. Statistical moments The statistical moments seem less suitable for the characterisation of the lead signal since they are dependent on the analyte concentration. The second moment is found to be strongly affected by the lead concentration but little by the interferents concentration. The signal becomes sharper for increasing lead concentrations. For the fourth moment, on the other hand, this is just the opposite. The first and third moments are affected by both factors. The fact that the statistical moments are dependent on the concentration while this is not the case for the time intervals can probably be explained by the shape of the signal. The lead signal consists of a strongly ascending atomisation part and a strongly descending diffusion part. As is illustrated in Fig. 4, in such a situation a small
broadening of the signal has little effect on the time intervals (At), but an important difference in the absorbance that is measured at each moment can be observed (AA), which is reflected in the second moment. 3.1.3. The slope of linear parts after linearisation
The concentration effect was eliminated by dividing the individual absorbances that constitute a signal by their maximal value. No reproducible linear parts can be found in the lead signal after a logarithmic transformation (In Ai). When a \Itransformation was applied, an important linear part can be distinguished in the atomisation part of the signal, while a small linear part can be found just after the maximum (see Fig. 5). The second derivative of the signal can be used to determine these linear parts. An important linear part at the end of the signal is found after a logistic transformation (Eq. 1). The speed of the appearance of the signal is significantly accelerated in the presence of K,SO, and
time
-I &&Aj))
I Fig. 5. Pure lead signal after a dq
transformation
together
with the second derivative of the signal.
W. Penninckx et al. /Chemometrics
and Intelligent Laboratory
Systems 23 (1994) 137-148
145
(a) .
350
300
250
. P
200
1,
150
f
. .
100
50
0
_--___--~--__-~-----~~~---~~-~~~~~~~~~~-------------------t
UCL
I
I
t
I
1 1
0.2
0.1
0
L I
03
Potassium sulphate concentration (%)
180
.
03
180
140
.
120
loo P 80
00
40
0
f 0
1
I
0.5
1
I
1.5
Sodium chloride concentration (%) Fig. 6. T2 value for signals measured in (a) different potassium sulphate concentrations and (b) different sodium chloride concentrations, calculated from the time intervals between the start of the atomisation cycle and the moment that l/e2 of the peak maximum is reached, the peak maximum and the decay to l/e2 of the peak maximum, together with the upper control limit.
146
W. Penninckx et al. /Chemometrics
and Intelligent Laboratory
Systems 23 (1994) 137-148
. (a)
* 1.5
.
t . f _--_----__---__----_--
;-----
. ----------------------------_--
.
&
: Ba 1
.
1
2
Potassium sulphate concentration (%)
0
.
-0.5
-1
t -1.5
r
__-_____-________--___--__--~____-___-_____-_________-___ __----
Bd
i _-__-_-___-____--_---~-__--__---____-____-~--
___-_
-2
-2.5
. &
-3 i
:
-3.5
Potassium sulphate concentration (%) Fig. 7. Slope of the Iinearised part in the atomisation different potassium chloride concentrations, together
stage of the signal (B,) and the diffusion stage (B,) of the signal measured with the upper and lower control limits (positioned at 3~).
in
W. Permit&x
et al. /Chemometrics
and Intelligent Laboratory
Systems 23 (1994) 137-148
slightly slowed down in the presence of NaCl. The speed of the diffusion is decreased by NaCl and hardly influenced by K,SO,.
mainly affects the atomisation diffusion stage of the signal.
3.2. Establishment of the control limits
4. Conclusions
Matrix-free reference solutions and monitored samples are measured in the same run, because as explained earlier the shape and position of the signals change during the lifetime of the tube. Since the use of Hotelling’s T2 requires that the number of replicate measurements of the reference solution substantially exceeds the number of control variables, only three variables were monitored: one in the atomisation stage, the peak maximum and one in the diffusion stage. Fig. 6 shows, for Pb in the presence of K,SO, or NaCl, the T2 values which are computed from the time intervals between the start and the atomisation cycle and (a> the moment that l/e* of the peak maximum is reached, (b) the peak maximum is reached and cc> the decay to l/e2 of the maximum, together with the upper control limits. All signals which are measured in the presence of K,SO, result in a T2 value above the upper control limit (Fig. 6a). Moreover a correlation can be seen between the K,SO, concentration and the T2 value. Although in all NaCl containing solutions signals were measured which are significantly different from the reference, no correlation can be observed between the NaCl concentration and the T2 value (Fig. 6b), which hampers the possible use of the T2 value to evaluate the effect of interferences on the quality of the determination. When the individual parameters are monitored, similar information is obtained. However, for some of the sodium chloride containing solutions, no abnormal values are found for the parameter related to the atomisation stage. Similar results are obtained when other time parameters were monitored. The investigated interferences are not reflected in the peak width. Monitoring the slope of the linearised part in the diffusion stage clearly permits the tracing of potassium sulphate interferences (Fig. 7b). The effect of K,SO, on the atomisation is less clear (Fig. 7a). Sodium chloride, on the other hand,
147
stage and not the
Interferences can be traced by comparing the lead signal with a reference signal, measured in a matrix-free environment. This was demonstrated for two important interfering salts. It is not clear if this can be generalised for other types of interferences. Good results are obtained when the different signal parameters are summarised in a Hotelling’s T2 value. For the moment we are investigating if this finding is confirmed for two other elements, namely aluminium, a less volatile element with different characteristics, and copper. One of the main problems is the changing of the shape of the signal during the lifetime of the tube, so that the monitored sample should be measured in the same run as the matrix-free reference. Moreover, the number of replicate measurements of the reference solution should substantially exceed the number of variables. Therefore it will be investigated if it is possible to standardise the signals that are measured at different stages of the lifetime of the tube, or even in different tubes of the same type, so that they can be compared. Until now control limits were used, which indicate that the measurement conditions are different from those in a matrix-free environment. In a further stage acceptance limits should be developed, which indicate up to which level acceptable interferences occur.
References [ll W. Penninckx, D.L. Massart and J. Smeyers-Verbeke, Effectiveness of palladium as a chemical modifier for the determination of lead in biological materials and foodstuffs by graphite furnace atomic absorption spectrometry, Fresenius' Journal of Analytical Chemistry, 343 (1992) 526-531. 121 W.B. Barnett and M.C. Cooksey, A study of graphite furnace peak shapes with a computer, Atomic Absorption Newsletter, 18 (1979) 61-64. [3] J.M. Harnly, Evaluation of graphite furnace atomic ab-
148
W. Penninckx et al. /Chemometrics
and Intelligent Laboratory
sorption signals using the peak shape and position, Journal of Analytical Atomic
Spectrometry,
3 (1988) 43-51.
[4] W. Wegscheider,
L. Jan%, M.T. Phe and M.R.A. Michaelis, Sensitivity estimation by the analysis of peak shapes in graphite furnace atomic absorption spectrometry, Chemometrics and Intelligent Laboratory Systems, I
(1990) 281-293. 151 G. Schlemmer and B. Welz, Palladium and magnesium
nitrates, a more universal modifier for graphite furnace atomic absorption spectrometry, Spectrochimica Acta, 41B (1986) 1157-1165. 161 J.E. Jackson, A User’s Guide to Principal
Wiley, New York, pp. 19-25.
Components,
Systems 23 (1994) 137-148
171 W.B. Barnett, W. Bohler, G.R. Canrick and W. Slavin,
Signal processing and detection limits for graphite furnace atomic absorption with Zeeman background correction, Spectrochimica Acta, 40B (1985) 1689-1703. [8] T.V. Karstang and O.M. Kvalheim, Sirius, a Program for Multivariate Calibration and Classification, University of Bergen, Bergen, 1990. [9] N. Dyson, Chromatographic Integration Methods, Royal Society of Chemistry, Loughborough, 1990, pp. 20-23. [lo] D.G. Kleinbaum, L.L. Kupper and H. Morgenstern, Epidemiologic Research, Van Nostrand Reinhold, New York, 1982, pp. 421-423.