Calibration methods – nomenclature and classification

CHAPTER 8 CALIBRATION METHODS – NOMENCLATURE AND CLASSIFICATION Paweł Kościelniak Institute of Analytical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Kraków, Poland

ABSTRACT Reviewing the analytical literature, including academic textbooks, one can notice that in fact there is no precise and clear terminology dealing with the analytical calibration. Especially a great confusion exists in nomenclature related to the calibration methods: not only different names are used with reference to a given method, but they do not express the principles and the nature of different methods properly (e.g. "the set of standard method" or "the internal standard method"). The problem mentioned above is of great importance. A lack of good terminology can be a source of misunderstandings and, consequently, can be even a reason of carrying out an analytical treatment against the rules. Finally, the aspect of rather psychological nature is worth to be stressed, namely just an analyst is (or should be at least) especially sensitive to such terms as "order" and "purity" irrespectively of what analytical area is considered.

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1 INTRODUCTION Reading the professional literature, one is bound to arrive at the conclusion that in analytical chemistry there is a lack of clearly defined, current nomenclature relating to the problems of analytical calibration. It is characteristic that, among other things, in spite of the inevitable necessity of carrying out calibration in instrumental analysis and the common usage of the term ‘analytical calibration’ itself, it is not defined even in texts on nomenclature problems in chemistry [1,2], or otherwise the definitions are not connected with analytical practice [3]. Another surprising fact is that in the face of the huge significance of calibration problems, they are treated too cursorily and quite inconsistently, even in textbooks on chemical analytics [4-6]. Most importantly, there is a lack of a universal classification of calibration methods which would be clear and logical enough so that, for example, the terms ‘calibration method’ and ‘analytical method’ are explicitly separate and relate to different fields of problems in analytical chemistry. The above-mentioned problem is undoubtedly of considerable significance. Lack of nomenclature ordering in the domain of calibration can become a source of numerous misunderstandings and obscurities, which, as a result, can cause improper or totally fallacious analytical proceeding. The situation is also unfavourable for didactic purposes, since it is difficult to credibly convey analytical knowledge on the basis of a particular textbook or academic script when using a language which is not only felt as incorrect, but which is also distinct from the one that can be found in other generally available sources. Finally, one ought to remember the psychological aspect: it is no-one else but the analytical chemist who is (or at least should be) particularly sensitive to ‘neatness’ and ‘order’, regardless of which fields of analytical chemistry the terms refer to. These problems were the chief reason that gave rise to this paper. The suggestions of definitions, terminology and classification of calibration terms made in this paper are the author’s own. They, however, met with understanding in the author’s closest academic society, and are being gradually introduced to the syllabus of analytical chemistry at the Faculty of Chemistry of the Jagiellonian University. Presentation of these suggestions to a large circle of analytical chemists has as its aim the initiation of a discussion which may shed some new light on the problems in question and contribute to the establishment of a generally accepted standpoint in this field. 2 ANALYTICAL CALIBRATION The basic analytical task consists in determining the concentration of a given substance (known as analyte) in a sample of the material being tested. It can only be done by using a chosen analytical instrument 1 and on the basis of the measurment data (the analytical signals) provided by the instrument for the sample.

1

Quantitative analysis of a sample is always carried out by means of a specific measuring instrument, although the devices used for this purpose are sometimes (in comparison with the commonly used nowadays, fully automated and computer-controlled apparatus of complex structure) so simple that their ‘instrumental’ character is no longer perceived and appreciated. These are, most importantly, the analytical balance and the burette, which are used for conducting respectively gravimetric and volumetrical analyses. From this point of view, there is no point in the commonly made division of chemical analysis into classical analysis (i.e. gravimetric and volumetrical) and instrumental analysis.

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Regardless of the instrument used in a particular case, the measured analytical signal (R) depends not only on the concentration of the analyte (ca), but also on a number of other factors. These include the parameters of the instrument (pa1, pa2, …, pam) and the factors determining the physicochemical conditions of the sample being analysed (pc1, pc2, …, pck), as well as the concentrations of other substances present in the sample (cd1, cd2, …, cdn), which are either natural components of the sample or which are added to it in the course of the analytical procedure. Thus, the general relation between the analytical signal and the aforementioned factors can be represented by the formula 2: R = f (ca; cd1, cd2, …, cdn; pa1, pa2, …, pam; pc1, pc2, …, pck)

(1)

Before the analytical signal is measured, the measuring instrument and the sample are adjusted to each other by setting the parameters determining the instrumental and physicochemical conditions at fixed, optimal levels 3. Thus, at the stage of making measurements, relation (1) takes a simplified form: R = f (K; ca; cd1, cd2, …, cdn)

(2)

where K is the parameter determining the general conditions of the analysis. The fundamental analytical problem is to determine the types and concentrations of the components (cd1, cd2, …, cdn) which influence the analytical signal that indicates the presence and concentration of the analyte in the sample. This influence is termed the interference effect, and the substances that cause the effect are called interferents. Although theoretically the interference effect may not occur or be negligible in a given case, it must always be reckoned with, at least because of the possibility of inserting the interferents into the sample when it is being prepared for the measurement. Accurate specification of the parameters determining the analytical conditions and determination of the types and concentrations of the interferents in the sample (cd1, cd2, …, cdn) on the basis of theoretical or even semi-empirical deliberations are always extremely difficult, and most often impossible. In consequence, direct determination of the concentration of the analyte in the sample on the basis of the analytical signal and by means of a precisely specified formula (2) is not possible either. Therefore, a purely empirical approach is used for this purpose, which is the domain of analytical calibration. The term ‘analytical calibration’ ought to be understood as denoting a process which consists in representing the actual (real, theoretical) dependence of the analytical signal on the concentration of the analyte (which in this context is called calibration function) in an empirical form (calibration plot4), and then using the plot to determine the 2

In some cases the analytical signal is not measured directly for the analyte, but for some other component which is added to the sample in a known quantity and which binds the analyte in a reaction of a known stoichiometry. Then, the signal depends additionally on the concentration of this component. However, since the presence of such a component in the sample is only of auxiliary character and serves the purpose of determining the concentration of the analyte, it has not been taken into account in the formula. 3 These activities when carried out in relation to the instrument are often also called ‘calibration’, which must not, however, be confused or identified with the concept of ‘analytical calibration’. 4 ‘Calibration function’ is more accurate, but due to the commonly accepted habit of representing calibration data in a graphical form, the term ‘calibration plot’ has been decided upon. 112

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concentration of the analyte in the sample under examination (i.e. obtaining analytical result). The calibration plot is constructed under specified, constant analytical conditions (both instrumental and physicochemical), with the use of one or several standard solutions 5, i.e. solutions of known, precisely determined concentrations of at least one component (usually analyte). Thus, analytical calibration consists of three stages: laboratory (i.e. the preparation of the standard solutions), measurement (i.e. the construction of the calibration plot) and mathematical (i.e. the calculation of the analytical result). A detailed mode of performing respective stages constitutes the calibration procedure. Each calibration procedure ought to be followed according to the strictly specified rules which determine a more general way of proceeding, leading to the attainment of (besides the main calibration objective) certain additional analytical goals. Such a specific mode of calibration procedure can be called a calibration method. 3 NOMENCLATURE OF CALIBRATION METHODS There are a number of different calibration methods used in chemical analysis. They appear in the literature under various, quite arbitrarily chosen names, which causes chaos and numerous misunderstandings. Two names, ‘standard series method’ and ‘calibration curve method’, are alternately made use of in reference to one commonly applied, conventional method. Neither of them, however, helps to distinguish this method from others, since, after all, there are other cases in which several standard solutions are prepared, and the calibration plot is always employed. The standard-addition method is often incorrectly termed ‘addition technique’, and frequently its version is unnecessarily and inconsistently distinguished as the ‘single addition method’. Some other terms, such as ‘internal standard method’, are conceptually incoherent and confusing, as here the word ‘standard’ refers to a specified quantity of a substance added to a solution of known analyte concentration (thus, one ‘standard’ is added to another ‘standard’). Such names of calibration methods as ‘dilution method’ [7,8] or the relatively recently introduced ‘addition and successive-dilution method’ [9] raise doubts as well, because they do not show correctly the differences between the methods. Other, less frequently used calibration methods, basically do not have fixed names, which contributes to still greater confusion. The above-mentioned problems seem to arise from the fact that the names of calibration methods refer, in the majority of cases, only to the laboratory stage of the calibration procedure, i.e. they emphasise either a particular way of preparing the standards (e.g. in the form of a series of standards or an internal standard) or the realisation of experimental procedure (e.g. addition of standards, dilution). Nevertheless, various methods are employed with the use of the same laboratory activities, while the calibration and analytical effects resulting therefrom are often totally different. The situation is further complicated by reports about analytical calibration in flow analysis [10-13]. Flow techniques offer so varied and different from the traditional ones ways of preparing solutions and making measurements that the newly elaborated calibration methods are usually given names that specify the procedures used. As a

5

A more general term is ‘standard sample,’ but in order to avoid confusion of this term with the real sample, and because of the common use of solutions in chemical analysis, the term ‘standard solution’ has been decided upon. 113

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result, it is sometimes even hard to make out on such grounds which analytical method is involved in a given case [14]. A very important analytical aspect related to the calibration problems, and thence also to the problems of nomenclature in this field, is the phenomenon of interference effect, which is fundamentally undesirable in chemical analysis. The effect can be minimised at the stage of preparing the sample for measurement by the separation of interferents from the analyte, using various techniques of separation of substances, or by adding to the sample a particular substance which chemically or physicochemically eliminates the influence of the interferent on the analyte. For various reasons, however, such processes may turn out to be hazardous, unreliable or utterly impossible to be carried out. In such cases, the last resort of overcoming the problem of the interference is to employ a proper calibration method. Given the lack of due classificatory and nomenclature order in regard to the calibration problems, there are, as can be observed, significant misunderstandings as to the practical possibilities of minimising interference effects by means of calibration. This is another important reason why it is necessary to come up with a new, clear classification of calibration methods, which would be helpful in fully solving these problems. 4 NEW CLASSIFICATION OF CALIBRATION METHODS The basis of the new classification of analytical methods is the aforementioned definition of analytical calibration, which assumes that the fundamental stages of the calibration are the representation of the calibration function and the means of calculating the analytical result. Thus, it has been posited that it is the computational and measurement aspects that should be the fundamental criteria for the diversification of calibration methods, rather than the laboratorial aspects (as in the hitherto prevailing approach). The above premise has led to the formulation of the thesis that all the calibration methods known in analytical chemistry can fall into three categories: interpolative, extrapolative and indicative [14]. The graphical interpretation of methods belonging to all three categories is shown schematically in fig. 1. In each case the analytical result (cax) is calculated by using the calibration plot, taking into account the analytical signal measured for the sample (Rx). In interpolative methods, the analytical result is calculated on the basis of the part of the calibration plot which encompasses a field determined in an experimental way, whereas in extrapolative methods, on the basis of the section which is beyond the field. In both cases, the plot in the section used for calculating the analytical result does not contain an experimental point with mathematical properties that distinguish it from other points.

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B

A R

R

Rx Rx

ca

cax

ca

cax

C R

Rx

cax

ca

Figure 1. The means of calculating the analytical result, cax, on the basis of the signal Rx related to the appropriate part of the calibration plot in an interpolative (A), extrapolative (B) and indicative method (C); R – analytical signal, ca – analyte concentration

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In indicative methods, the analytical result is calculated on the basis of the location of the characteristic point on the calibration plot, the point being different (from the mathematical point of view) from the other points comprising the plot. 5 INTERPOLATIVE METHODS There are four different interpolative calibration methods used in analytical practice; they can be called: • CIM, ‘Conventional Interpolative Method’; • IIM, ‘Indirect Interpolative Method’; • IISM, ‘Interpolative Internal Standard Method’6; • IDM, ‘Interpolative Dilution Method’. The principles that underlie each of these interpolative methods are shown in figure 2. The CIM method is identical to the most commonly adopted calibration approach, popularly known as the ‘standard series method’ or the ‘calibration curve method’. This method usually involves the preparation of several standard solutions of various, known concentrations of the analyte. These solutions as well as the sample being examined undergo the measurement of the analytical signal under analyte-specific conditions. Making measurements separately for each standard solution and for the sample makes it possible to calculate the analytical result in the interpolative way (see figure 2A). In flow analysis, there are numerous instances of employing the CIM method with a series of standard solutions generated from a single solution [15-17]. In some cases, the solutions prepared in this way cannot be assigned an exactly determined analyte concentration; then, the calibration function is represented in the form of a network of linear calibration plots [18,19]. There is also such a version of the CIM method in which the standard solutions are added to the sample (in the flow injection mode), making it possible, however, to make measurements for all of the solutions separately [20]. Nevertheless, none of these modifications changes the character or the essence of the CIM method. The IIM method is applied when the instrument being used does not allow the measurement of the analytical signal for the analyte but it is possible to measure the signal for some other substance which can enter a chemical reaction with the analyte. Then, a constant, known amount of the reactant is added both to the sample and to the standard solutions of increasing analyte concentration. If the reactant is added in an excessive amount in proportion to the highest analyte concentration, the measurement of the signals for the reactant left after the reaction in each standard solution leads to the construction of a calibration plot with the shape presented in fig. 2B7. Calibration with the use of the IIM method can contribute to the enlargement of the number and types of substances that can be marked with a given analytical method. A typical example of such possibilities is the use of the IIM calibration to mark anions by means of atomic absorption spectrometry [21]. The difference between the IISM method (commonly known as the ‘internal standard method’) and the CIM method is that the standard solutions and the sample are 6

It seems that the term ‘internal standard’ used in reference to an analytical method is so deeply rooted in the consciousness of chemical analysts that an attempt to change it would be vain. 7 It is also possible to use the principle described to prepare the standard solutions in such a way that the calibration plot has an upward ‘climb’. 116

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supplemented with another substance (the so-called internal standard) of an unchanging, known concentration, and the measurements are made for all of the solutions under conditions specific to both the analyte and internal standard. The analytical signal is assumed to be the proportion of the signals received in both cases (see figure 2C). The principal objective of the IISM method is the determination of analyte concentration in the sample with increased precision, since it is assumed that if the internal standard and the analyte have similar chemical properties, the size and direction of random changes of the analytical signals measured for both components are similar as well. In such a case, there is a good chance that the proportion of both signals will be characterised by considerably smaller fluctuations than a single signal measured for the analyte, which in consequence will allow the minimisation of the error of a random analytical result. In the IDM method, a single standard solution containing analyte is used. Both the standard and the sample are progressively diluted, and at each dilution stage both solutions are measured under conditions specific to the analyte. Each pair of analytical signals received allows to interpolatively determine analyte concentration in the sample of a given dilution (the so-called apparent concentration) with the help of a two-point calibration plot (see figure 2D). The set of the apparent concentrations obtained is interpreted in the following way [8]: a) if the values of the apparent concentrations are statistically the same, the analytical result is calculated from the mean of these concentrations b) otherwise the boundary value of the apparent concentration (in a sample of an infinitely high concentration) is determined, and it is accepted as the analytical result. The dilution method is applied in particularly difficult and not wholly recognisable analytical conditions, i.e. when there is a risk that the measurements are made in a non-linear range of the calibration function and when there is the interference effect. This is because it is assumed that in the course of diluting the sample both effects gradually abate, and disappear completely at an infinitely high dilution of the sample, thereby allowing accurate determination of the analytical result. The IDM method has also been elaborated in flow analysis, by carrying it out in the continuous flow technique [22] and flow injection technique [23,24].

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B

A Ra

Rb

RaN

Rb0

~ Rb1

Ra3

Rbx Rb2

Ra2 Rax

Rb3

~

Ra1

RbN Ra0 0

ca1

cax

ca2

ca3

~

ca 0

caN

ca1

cax

ca2

ca3

~

ca caN

D

C Ra/Rs

Ra

(Ra/Rs)N

Ra1

~ (Ra/Rs)3

Ra2 Ra3

(Ra/Rs)2

Rax1 RaN Rax2 Rax3 RaxN

(Ra/Rs)x (Ra/Rs)1

(Ra/Rs)0

0

ca1

cax

ca2

ca3

~

ca caN

R0

ca 0

cax

ca1

Figure 2. Interpolative method principle: CIM (A), IIM (B), IISM (C) i IDM (D); Ra, Rb, Rs – signals measured respectively for the analyte, for the substance reacting with the analyte and for the internal standard; z, | – experimental points obtained respectively for the standard solutions and for the samples; (the remaining symbols as in fig.1.)

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6 EXTRAPOLATIVE METHODS All interpolative methods can be applied in the extrapolative version. Thus, it can be said that the extrapolative methods include: • CEM, ‘Conventional Extrapolative Method’; • IEM, ‘Indirect Extrapolative Method’; • EISM, ‘Extrapolative Internal Standard Method’; • EDM, ‘Extrapolative Dilution Method’ The graphical interpretation of the extrapolative methods is presented in figure 3. The fundamental condition for an interpolative method to become extrapolative in character is the performance of measurements for the sample alone and for the sample with at least one addition of a standard solution containing analyte. The solutions undergoing measurement must be prepared in such a way that the concentration of the ‘part’ of the analyte which is naturally contained in the sample is equal in these solutions. The calibration plot constructed on the basis of the measurement data is in this case within a limited range of analyte concentrations, i.e. from the concentration of the analyte in the sample up to the aggregate concentration of the analyte in the sample and in the addition with the highest analyte concentration. Therefore, the determination of the analytical result is possible only through the extrapolation of the plot (see figure 3). Each interpolative method having assumed the extrapolative character can be carried out (at the laboratory, measurement and calculation stage) in its typical way, thereby realising its specific (aforementioned) objectives and tasks. The conventional calibration method in the extrapolative version (CEM) is called ‘standard-addition method’ and, as is known, is commonly applied in chemical analysis. It is most often carried out according to the traditional procedure, including, among other things, the preparation of a series of solutions of the sample with successive additions of a standard of various concentrations and making measurements separately for each solution. In flow analysis, multiple modifications of this procedure are proposed; they are to improve the efficiency at both the laboratory and the measurement stage [10,11]. The EDM method has also found its use in analytical practice, and in the literature it is termed ‘addition and successive-dilution method’ [9] or simply ‘addition and dilution method’ [25]. This method has recently been introduced into flow analysis as well. [26]. The author is not familiar with any instances of the application of the IEM or EISM method in analytical calibration (although, obviously, he does not exclude the existence of such reports). There can be no doubt, however, that the application of these methods is real, hence their presence on the list of methods subject to the classification proposed.

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B

A Ra

Rb Rb0

RaN

~ Ra2 Rbx Ra1

Rb1

Rax

Rb2

~ RbN Ra0 -cax

0

∆ca1

∆ca2

~

∆ca -cax

∆caN

0

∆ca1

∆ca2

~

∆ca ∆ca3

D

CC Ra/Rs

Ra

(Ra/Rs)N

Ra1

~ (Ra2/Rs)2

Ra2

(Ra/Rs)1

Ra3

(Ra/Rs)x

RaN RaxN Rax2 Rax3 Rax1

(Ra/Rs)0 -cax

0

∆ca1

∆ca2

~

∆ca -cax

∆caN

R0 0

∆ca ∆ca1

Figure 3. Extrapolative method principle: CEM (A), IEM (B), EISM (C) i EDM (D);

∆ca – the concentration of the analyte added to the sample (the remaining symbols as in the previous figures)

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7 INDICATIVE METHOD The indicative method encompasses all of the titration 8 techniques applied in chemical analysis. The basis of titration is the chemical reaction that takes place between analyte and one of the constituents of the standard solution (titrant). The calibration plot (the socalled titration curve) is usually constructed on the basis of the analytical signals measured after the continuous addition of portions of the standard solution to the sample (or vice versa). The measurements are made under the conditions specific to a chosen substance taking part in the reaction (either product or reagent). The concentration of the analyte in the sample is calculated on the basis of the value of the volume of the standard solution (or the sample) corresponding to the endpoint of titration (see fig. 4).

Rbx

V 0

Vx

0

cax

ca

Figure 4. Titration as an indicative calibration method: V – volume of the standard solution (titrant), Vx – volume of the titrant in the endpoint (|) of titration; z experimental points obtained in the course of titration

8

Titration is commonly considered to be one of the small number of ways of direct (non-calibration) determination of analyte concentration in a sample. I should be noticed, however, that this concentration cannot be revealed without the knowledge of the concentration of this component of the titrant which reacts with analyte. Thus, treating titrant solution as a standard solution, and the process of titration as an empirical calibration process, is, in the author’s view, fully justified. 121

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According to the criteria of the new classification of calibration methods, titration constitutes a totally distinct analytical calibration method. Both the basis and the characteristic feature of this method is chemical reaction. Although reaction is also a fundamental element of the indirect interpolative method (IIM), in titration, unlike in the IIM method, the course of reaction is registered continuously until a particular state corresponding to the endpoint is achieved. Another difference is that the analytical result of titration depends on the knowledge of the stoichiometry of the reaction, whereas in the case of the IIM method this information can be unknown. An altogether peculiar feature of titration is the possibility of determination of analyte concentration in the sample without the use of an instrument measuring the analytical signal: due to the fact that to achieve this purpose it is enough to determine a particular state of the chemical reaction taking place, in appropriate chemical conditions this state can be ‘caught’ visually. 8 CALIBRATION METHODS AND INTERFERENCE EFFECT The classification of calibration methods has a separate justification from the point of ‘immunity’ of the respective categories of calibration methods to the interference effects that take place. Using the conventional interpolative method (CIM) for calibration, one can expect a relatively greatest threat from the interference effect. It results from the fact that the calibration function corresponding to the sample with interferents cannot be accurately represented with a calibration plot constructed with the use of standard solutions containing analyte alone. Therefore, if the signal measured for the sample, triggered off by the analyte and changed by interferents, is related to such a calibration plot, one has to reckon with the fact that the analytical result obtained will be burdened with an error. Such a situation is shown in figure5. The above principle applies to the other interpolative methods as well, although their specific features reduce the greatness of the problem. In the case of the indirect interpolative method (IIM) the signal is not measured directly for the analyte, but for an ‘alien’ component added to the sample and to the standard solutions. So, there is a chance that this component will bind the analyte in both environments in amounts expected, thereby making it free from the presence of interferents. On the other hand, though, one must be careful so that the components present in the sample do not take the role of interferents against the component which is added. When calibration is carried out with the use of the interpolative internal standard method (IISM), one can hope that the interferents present in the sample will cause the same (in respect of direction and size) change of the signals measured for the analyte and internal standard. In such a case, the proportion of both signals will not show any interference effect. Given a substantial specificity of these effects, however, there can be justifiable doubts as to whether the selection of an internal standard working in this way is real. Calibration with the use of the interpolative dilution method (IDM) has as its aim the elimination of interference effects. This task follows from the assumption that these effects gradually diminish in the course of diluting the solution of the sample. It has been proved experimentally [27,28], however, that this assumption does not always come true. Furthermore, it has been proved that the dilution of a sample can make the interference effect increase, leading to the determination of analyte concentration with greater error (using IDM) than in the case of a sample which has not been diluted [27].

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Ra

a a’

Rax

ca 0

cax

cax’

Figure 5. CIM method: incorrect representation of the calibration function (a) with the use of the calibration plot (a’) as a result of the interference effect and the resulting analytical error (cax’ ≠ cax) The only fully effective way of minimising of interference effects that is universal to all of the interpolative methods consists in a minute representation of the composition of the sample in the standard solutions in respect of the type and concentration of the interferents. Only then can the calibration function corresponding to the composition of the sample be accurately represented with the use of a calibration plot. This, in practice, requires the identification of which components of the sample in a given case play the role of interferents, and the addition of them to all of the standard solutions in such concentrations in which they occur in the sample. Naturally, the task is extremely difficult and possible to accomplish entirely only in the case of small interference effects caused by single components of the sample. It can be generally affirmed that the possibility of the elimination of interference effects with the use of interpolative calibration methods is greatly limited. The conventional extrapolative method (CEM) in its principle represents a way of compensation for interference effects. When the standard solutions have been added to the sample, the analyte is in the natural environment of the sample, and thereby in the presence of possible interferents with ideal regard to their type and concentration. As a result, the calibration plot should also ideally represent the calibration function, and the analytical result that has been calculated ought to be accurate (see figure 6).

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Ra b a

a’

Rax a’ b

∆ca -cax’

-cax

0

Figure 6. CEM method: a faithful representation of the calibration function (a) with the use of the calibration plot (b) as a result of the compensation for the interference effect, and an incorrect representation (a’) as a result of the different behaviour of the analyte in the sample and in the standards, and the ensuing analytical error (cax’ ≠ cax) The fundamental principle of the other extrapolative methods is the same as that of the CEM method. Thus, it can be supposed that they are equally able to compensate for interference effects. Moreover, their specific properties can be as much additionally helpful in this field as the analogous interpolative methods in relation to the CIM method (it has recently been proved experimentally in the case of calibration with the use of the extrapolative dilution method (EDM) applied in flow analysis[26]). On the other hand, the CIM method has various limitations in the scope of the minimisation of interference effects. One of them is the fact that the analyte added to the sample may have a different chemical form from the analyte naturally contained in the sample [29]. Then, both forms of analyte can be subject to the influence of interferents in different degrees, which in consequence will make it impossible to faithfully represent the calibration function (see fig. 6.). This problem certainly applies to the other extrapolative methods as well. It appears that the method which is the most ‘resistant’ to interference effects is the indicative method. There are a number of special factors that favour this feature: a) the standard solution is added to the sample (being placed in the natural environment of the interferents present in the sample), b) the standard solution added to the sample does not contain analyte (so there is no risk of adding analyte in an inappropriate chemical form), c) a particular component of the standard solution reacts with the analyte present in the sample (relieving the analyte from the activity of interferents).

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The occurrence of chemical reaction in the calibration procedure of titration is of particularly great significance from the point of view of the elimination of interference effects. That is because the standard solution can be, to a vast extent, selected in such a way that the reaction is as specific as possible in relation to the analyte. Unfortunately, titration cannot be applied in many analytical methods (e.g. in those which do not use liquid solutions or in which the measuring instrument is not able to react only to a chosen analyte form participating in the chemical reaction). Although there are many advantages which in many respects (not only of the high ‘resistance’ to the impact of interferents) place titration above other calibration methods, this is to be regretted. 9 MIXED CALIBRATION METHODS Finally, two other approaches to calibration should be mentioned. They are used in analytical practice but are not directly placed in the classification of calibration methods which has been proposed. One of these procedures consists in choosing one from a series of samples of similar chemical composition and analysing it with the use of the conventional extrapolative method (CEM). The calibration plot constructed at this stage and extended by the extrapolated section is used to mark interpolatively (by means of CIM method) analyte in other samples. This is illustrated in figure 7.

Ra

(Rax)II

(Rax)I

(Rax)III

∆ca (-cax)I

(-cax)III

0

(-cax)II

Figure 7. The extrapolative-interpolative method: calibration plot obtained by means of the CEM method is used to extrapolatively determine analyte concentration (cax)I_in a chosen sample and to interpolatively determine concentrations (cax)II and (cax)III in two other samples.

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The calibration procedure described has as its foundation the assumption (which is, naturally, not always true) that the calibration function obtained, which allows for the presence of interferents in the sample chosen, is identical to the functions corresponding to the other samples. On the other hand, the application of such a procedure in the case of serial analyses, instead of the conventional extrapolative method (CEM) used in relation to each sample, saves both time and effort. The above method mixes the calibration procedures typical of the CEM and CIM methods; therefore it can be called the extrapolative-interpolative method. Another interesting case of calibration is the indicative method in the version adapted to flow analyses. The calibration procedure in this case is usually as follows: the standard solution is dosed in a specified portion into a continuous flow of the solution of the sample (or vice versa) coming to the measuring instrument [30]. As a result of the chemical reaction occurring in the course of the process, a calibration plot with the characteristic shape of a cut peak is plotted (see figure 8). Although the signal (or even two signals) corresponding to the endpoint can be identified on such a plot, it is practically impossible for such a signal to be assigned an accurate value of the volume of the solution added at the moment, or for the analytical result to be calculated in the way typical of the indicative method.

R ∆t

t Figure 8. Calibration plot (the function of the analytical signal R and time t) in the indicative method used in flow injection analysis and the way of determining the endpoint of titration (PK); the width of the peak (∆t) corresponds to the value of analyte concentration in the sample In order to solve this problem, the fact is used that the width of the peak corresponds to the concentration of the analyte in the solution undergoing the test. This entails the preparation of a series of new standard solutions - this time containing only analyte of different, exactly determined concentrations - which are successively inserted into the flow system before the introduction of the sample. The measurement of the width of the peaks that have been plotted can be used to construct a conventional calibration plot, which then is used to interpolatively determine analyte concentration in the sample. The method described links the procedures of the indicative and CIM method, and can therefore be called the indicative-interpolative method.

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10 CONCLUSIONS The new classification of calibration methods together with the nomenclature of calibration concepts which has been proposed undoubtedly contribute to the ordering of different calibration methods offered in the analytical literature. The methods classified are characterised by their particular, specific properties, which clearly distinguish them from one another. These characteristics are presented in table 1. TABLE 1. Characteristic properties of calibration methods Method

Calibration plot construction

Calculation of the analytical result Interpolative on the basis of the measurement results interpolatively, by means obtained separately for the standard solutions of the calibration plot (less frequently for a single standard solution) containing analyte and for the solution of the sample Extrapolative on the basis of the measurement results extrapolatively, by means obtained for the standard solutions (less of the calibration plot frequently for a single standard solution) containing analyte, added to the solution of the sample means of the Indicative on the basis of the measurement results by obtained as a result of the chemical reaction calibration plot on the that takes place between the analyte contained basis of the location of the in the solution of the sample and a component characteristic experimental (not analyte) of a single standard solution point progressively mixed with the sample

The classification proposed is open. This means that it does not rule out the possibility of developing other calibration methods and the fact that these new methods may have somewhat different properties from those listed above. It seems, however, that the introduction of such other methods could not undermine the legitimacy or change the general division of all methods into three categories: interpolative, extrapolative and indicative. What is interesting is the fact that this taxonomy makes it possible, to a certain degree, to predict the possibility of performing calibration in a new way (it concerns, for example, certain extrapolative methods which are analogous to the interpolative ones), and, as it appears, it can provide motivation for making new attempts at combining different calibration methods. Thus, the deliberations presented may affect the direction and development of experimental research in the domain of analytical calibration. Another consequence of the acceptance of this approach to calibration problems is the possibility of introducing certain crucial, logical changes into the classification of analytical methods. If one agrees with the fact that titration is a calibration method, then the presentation of instrumental titration techniques in the form of distinct analytical methods (e.g. amperometric titration) [ ], or contrasting them within a given method with the direct techniques (e.g. direct conductometry or conductometric titration) [ ] is no longer sensible. It seems reasonable that in a textbook description of analytical

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methods, each of them should be given a paragraph on the application, in a given case, of different calibration methods, taking into account the technique of titration. The classification may, therefore, have far-reaching analytical consequences in the field of application and didactics. It appears that this is a ‘merit’ not of this particular classification itself, but of the fact that any classification has been introduced. This confirms the necessity of taking such actions in this and other fields of analytical chemistry. The above remark has a wider and more general aspect. Namely, analytical chemists’ tasks are too often reduced to purely experimental activities, and analytical chemistry is treated only as chemical analytics, i.e. a discipline that plays a service and auxiliary role in other fields of chemistry, or even beyond it (e.g. in biology, geography or environmental studies)9. It is forgotten that analytical chemistry is a separate science and as such, it requires the development and modification of the rules, principles and methods on which it is based. The deliberations presented in this paper exemplify the need to be aware of this naturally, obvious, truth. BIBLIOGRAPHY [1] Słownik chemii analitycznej, WNT, Warszawa 1984 [2] Słownik Chemiczny, Wiedza Powszechna, Warszawa 1995 [3] Danzer K. , and Currie L.A. , Pure & Appl. Chem., 4, 993 (1998) [4] Minczewski J. , and Marczenko Z. , Chemia analityczna, t. I–III, PWN, Warszawa 1985 [5] Szczepaniak W. , Metody instrumentalne w analizie chemicznej, Wydawnictwo Naukowe PWN, Warszawa 2002 [6] Cygański A. , Metody spektroskopowe w chemii analitycznej, WNT, Warszawa (1993) [7] Gilbert Jr. P.T. , Anal. Chem., 31, 110 (1959) [8] Kościelniak P. , Zesz. Nauk. UJ, 36, 27 (1993) [9] Pszonicki L. , and Skwara W. , Talanta, 36, 1265 (1989) [10] Fang Z. , Flow Injection Atomic Absorption Spectrometry, Wiley, Chichester 1995, 203 [11] de la Guardia M. , FIA Strategies for Calibration and Standarization in Atomic Spectrometry, in: Flow Analysis with Atomic Spectrometric Detectors, A. SanzMendel (ed), Elsevier, Amsterdam, 1999, 98 [12] Tyson J. F. , Spectrochim. Acta, 14, 169 (1991) [13] Trojanowicz M. , and Olbrych-Śleszyńska E. , Chem. Anal.(Warsaw), 37, 111 (1992) [14] Kościelniak P. , Anal. Chim. Acta, 438, 323 (2001) [15] Agudo M. , Rios A. , and Valcarcel M. , Anal. Chim. Acta, 264, 265 (1992) [16] Krieger B.L. , Kimber G.M. , Selby M. , Smith F.O. , Turak E.E. , Petty J.D. , and Peachey R.M. , J, Anal. At. Spectrom., 9, 267 (1994) [17] Kościelniak P. , Herman M. , and Janiszewska J. , Lab. Robot. Autom., 11, 111 (1999) [18] Tyson J.F. , and Bysouth S.R. , J. Anal. At. Spectrom., 3, 211 (1988)

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The evidence for such a situation is the attitude of the editors of numerous chemistry journals of analytical character, who generally do not accept purely theoretical or conceptional papers for publication, even when the proposed deliberations and hypotheses advanced do not require experimental evidence or it is impossible to provide such evidence instantly. 128

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[19] Kościelniak P. , Janiszewska J. , and Fang Z. , Chem. Anal. (Warsaw), 41, 85 (1996) [20] Tyson F.J. , Anal. Proc., 18, 542 (1981) [21] Absorpcyjna spektrometria atomowa, M. Pinta (ed), PWN, Warszawa 1977, 368 [22] Kościelniak P. , Kozak M. , and Karocki A. , Chem. Anal. (Warsaw), 41, 363 (1996) [23] Fan S. , and Fang Z. , Anal. Chim. Acta, 241, 15 (1990) [24] Sperling M. , Fang Z. , and Welz B. , Anal. Chem., 63, 151 (1991) [25] Kościelniak P. , and Walas S. , Zesz. Nauk. UJ, 36, 53 (1993) [26] Kościelniak P. , and Kozak J. , Anal. Chim. Acta., 460, 235 (2002) [27] Kościelniak P. , Sperling M. , and Welz B. , Chem. Anal., 41, 587 (1996) [28] Kościelniak P. , Anal. Chim. Acta, 367, 101 (1998) [29] Welz B. , Fresenius Z. Anal. Chem., 325, 95 (1986) [30] Růžička J. , and Hansen E.H. , Flow Injection Analysis, John Wiley, New York 1988, 47

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