Alicia gy aryghy I ACKa6pR 02, 2010 413 pagos Analytical Chemistry Theoretical and Metrological Fundamentals K Danzer Analytical Chemistry Theoretical and Metrological Fundamentals With 138 Figures and 31 Tables K. Danzer Am Friedensberg 4 07745 Jena Germany e-mail: claus. danzer@jetzweb. de Library of congress control Number 2006932265 ISBN-IO 3-540-35988-5 Sprin er Berlin Heidelber NewYork ISBN-13 978-3-540-35988-3 s or413 10. 1007/b103950Thi S»ipe to View are reserved, w hethe he wh concerned, specificall reuse of illustrations, o New York DOI right.

All rights e material is n, reprinting, reproduction on icrofilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Vlolations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springer. om Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt rom the relevant protective laws and regulations and therefore free for general use. Product liability: The publishers cannot guarantee the accuracy of any information about dosage and application contained in this book. In every individual case the u user must check such information by consulting the relevant literature.

Cover-Design: WMXDesign GmbH, Heidelberg Typesetting: PTP-Berlin Protago-TEX-Production GmbH, Germany production: LE-TEXJelonek, Schmidt & Vockler GbR, Leipzlg, Germany Printed on acid-free paper 2/3141/YL – 5432 1 0 Analytical chemistry can look back on a long history. In the ourse of its development, analytical chemistry has contributed essentially to the progress of diverse Felds of science and technology. Signi- cant progress in natural philosophy, chemistry and other disciplines has been founded on results and discoveries in analytical chemistry.

Well known examples include Archimedes principle, iatrochemistry, emergence and overcoming of phlogiston theory, basic chemical laws on stoichiometry and mass proportions as well as the discoveries of elements and of nuclear ssion. As chemistry Split into inorganic, organic and physical chemistry in the middle of the nineteenth century, the uestion occasionally arose as to whether analytical chemistry was likewise an autonomous -eld of chemistry. At the beginning of the twentieth century, analytical chemistry was establlshed by Wilhelm Ostwald and other protagonists on the basis of chemical and physicochemical laws and principles.

In addition, analytical procedures and instruments spread into other chemical -elds. However, in the 1 gsos and 1960s a new generation of analysts opened their mind to ideas coming from other scienti*c -elds dealing with measurements from Ether points of View such as information science, metrology, technometrics, etc. As a result, efforts made towards the acceptance of a 413 efforts made towards the acceptance of analytical chemistry as an autonomous -eld of chemistry increased.

Analysts in USA and Europe founded organisations and forums that focussed ideas and developments in progressive directions. In this way, not only were national and international societies formed but also regular conferences like Pittcon and Euroanalysis. In this connection the so-called Lindau circle should be mentioned where analysts from Germany, Austria and Switzerland made public relevant fundamentals of analytical chemistry derived from tatistics, information theory, system theory, signal theory, game theory, decision theory, metrology, etc.

In parallel with this, such modern pnncples have been successfully applied in selected case Studies, mainly by scientists from USA, UK, and Canada. From this development, real theoretical and metrological fundamentals of analytical chemistry have crystallized. However, the acceptance of analytical chemistry as an automomous branch of chemistry has not been realised. Gradually, however, progress in analytical chemistry culminated in the 1990s in the proclamation of a new scienti- c discipline, analytical science.

Protagonists of these ctivities included Michael Widmer and Klaus Doerffel. Today, analytical chemistry is Still a discipline within chemistry. Although characterized as an auxiliary science, analytical chemistry continues to develop and grow just as before. It is no detraction being characterized as an auxiliary discipline as mathematics shows. However, it is likely that efforts to make 3 413 auxiliary discipline as mathematics shows. However, it is likely that efforts to make analytical chemistry a more Independent science Will be repeated in the future from time to time.

Analytical chemistry possesses today a sound basls of chemical, physical, ethodical, metrological, and theoretical fundamentals. The • rst of these are usually taken as the basis of classical textbooks on analytical chemistry. The others are found in diverse publications in the – eld of analytical chemistr•y and chemometrics. It is essential to state that chemometrics is not the theoretical basis of analytical chemistry but it contributes signi- cantly to it. Frequently, analytical chemistry is considered to be a measuring science in chemistry.

Therefore, its object is the generation, evaluation, interpretation, and validation of measuring signals as well as the characterization of their uncertainty. With this aim, the analyst needs knowledge of the general analytical process, statistics, optimization, calibration, chemometrical data analysis, and performance characteristics. In this book the attempt is made to summarize all the components that can be considered as building blocks of a theory of analytical chemistry.

The uilding» constructed in this way is a provisional one. It is incomplete and, therefore, extension, reconstruction and rebuilding have to be expected in the futura A large number of mathematical formulas Will be found in the book. This may be regarded as a disadvantage articularly because some of them are not readily to apply in daily analytical practice. However, great scientists, explicitly Emanuel Kant, said that a scienti-c branch 4 413 practice.

However, great scientists, explicitly Emanuel Kant, said that a scienti c branch contains only so much of science as it applies mathematics. Consequently, all the relationships which can be described mathematically should be so described. It is true despite Werner Heisenbergs statement: Although natural processes can be described by means of simple laws which can be precisely formulated, these laws, on the other hand, annot directly be applied to actions in practice.

Wherever possible, of- cial de nitions of IUPAC, ISO and other international organizations have been used, in particular in the Glossary of Analytical Terms» compiled at the end of the book. However, uniformity could not be achieved in every case. In a few instances, special comments and proposals (characterized as such) have been added. Although progress in the eld of harmonization of nomenclature and de nitions has been considerable, sorne things Still remain to be done. Some of the contents of various sections have been published previously and are, of course uoted verbatim.

In this connection the author is grateful to Klaus Doerffel, Karel Eckschlager, Gunter Ehrlich, Andrzej Parczewski, Karol Florian, Mikulas Matherny, Gunter Marx, Dieter Molch, Eberhard Than, Ludwig Kuchler and others for long-standing collaboratlon resulting In mutually complementary papers and books. A chapter on statistics was previously published in another book (Accreditation and Quality Assurance Preface VII in Analytical Chemistry edited by Helmut Gunzler at Springer). Gratefully I have adapted essential parts of the translation of Gaida Lapitajs here in this book.

Stim 413 ave adapted essential parts of the translation of Gaida Lapitajs here in this book. Stimulations and ideas have arisen from discussions with William Horwitz, Duncan Thorburn Burns, Alan Townshend, Koos van Staden, and other members of diverse IIJPAC Commissions and Task Groups as well as of- cers of the Analytical Chernistry Division- From a 20-year membership of various IUPAC bodies I have gained a variety of feedback and experience which has proved to be useful in the writing ofthis book. In particular, owe Lloyd Currie and Mattias Otto a great debt of gratitude.

They have permitted me to use essential arts of common publications on calibration quoted in Chap. 6. Many of the results stem from work carried out with colleagues, collaborators, postdocs and graduate students. All of them are deserving of my thanks but, due to the large numbers involved, this cannot be done here. Some representative colleagues include Jurgen Einax, Hartmut Hobert, Werner Schron, Manfred Reichenbacher, Reiner Singer, Dietrich Wienke, Christoph Fischbacher, Kai-Uwe Jagemann, Michael Wagner, Katrin Venth, Raimund Horn, Gabriela Thiel, Demetrio de la Calle GarcÃa, and Balint Berente.

The author gratefully acknowledges the ooperation with and the support of the editorial staff of Springer. particularly I have to thank Peter Enders, Blrgit Kollmar-Thoni, and { last but not least {John Kirby, the English copy editor, who has essentially improved the English. Many thanks for that. No book is free of errors and this one Will be no exception. Therefore, the author would be grateful to readers who point out errors and mistakes and suggest any improvement. Jena, Ju would be grateful to readers who point out error s and mistakes and suggest any improvement. Jena, July 2006 Klaus Danzer Contents Symbols . . .

XIII Abbreviations and Acronyms . XXVI 1. 1 1. 22 2. 1 2. 2 2. 3 2. 43 3. 1 3. 2 3. 3 3. 4 3. 544. 1 4. 1. 1 4. 1. 2 4. 2 4. 3 4. 3. 1 4. 3. 2 4. 3. 3 4. 3. 4 Object of Analytical Chemistry . , De -nition of Repertoire of Analytlcal Chemistry References .. The Analytical Process Principles of Sampling . Sample Preparation _ Principies of Analytical Measurement . Analytical Evaluation — References Signals in Analytical Chemistry Signals and Information . Analytical Signals . Types and Properties of Anal . . Types and Properties of Analytical Signals . Analytical Signals and Information . Model of Signal Generation . Dimensionality of Mathematical Statistical Evaluation of Analytical Results Reliability of Analytical Observations and Measurements … Systematic Deviations . Random Variations . Uncertainty Concept Statistical Tests , Null Hypotheses . Test for Measurement Series . Comparison of Standard Deviations .. Comparison of Measured Values . 11 5 10 13 15 23 26 31 37 43 43 4447 53 60 63 65 65 67 69 75 78 79 80 81 82 x 4. 4 4. 5 4. 5. 1 4. 5. 2 4. 5. 3 4. 5. 4 Reliability of Qualitative Analytical Tests .. Statistical Quality Control Quality Criteria for Analytical Results Attribute Testing . 8 413 . . Attribute Testing .

Sequential Analysis Statistical Quality Control . Studying In uences and Optimizing Analytical Procedures Testing the Signi-cance of In uencing Factors . Analysis of Variance (ANOVA) Experimental Design Optimization of Analytical Procedures . Global Optimization by Natural Design Calibration In Analytical Chemistry . General Fundamentals of Calibration Fundamental and Experimental Calibration The General Three-Dimensional Calibration Model Regression and Calibration Single Component Calibration . Linear Calibration Model Errors in Linear Calibration Weighted Linear Least Squares Estimation ( g 413 Least Squares Estimation (WLS) .

Weighted Linear Linear Least Squares Fitting in Case of Errors in goth Variables . Statistical Tests and Validation of Calibration . Alternative Calibration Procedures Nonlinear Calibration . Multisignal Calibration Multicomponent Calibration . Classical Multivariate Calibration . . Inverse Calibration , Validation of Multivariate Calibration Calibration by Arti- cial Neural Networks Analytical Performance Characteristics Reliability of Analytical Measurements . Precision Precision ofTrace Analyses . Accuracy and Trueness 85 90 90 92 93 95 98 101 101 101 108 112 116 120 123 124 124 26 127 130 130 134 137 138 140 144 151 152 155 157 15