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. Chapter 8 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. 111 Chapter 8 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 Chapter 8 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