Januar11981 on the Derivation of a Creep Law from Isothermal Bore Hole

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Januar11981 on the Derivation of a Creep Law from Isothermal Bore Hole JANUAR11981 ON THE DERIVATION OF A CREEP LAW FROM ISOTHERMAL BORE HOLE CONVERGENCE BY J. PRIJ J.H.J. MENGELERS ECN does not assume any liability with respect to the use of, or for damages resulting from the use of any information, apparatus, method or process disclosed in this document. Netherlands Energy Research Foundation ECN P.O. Box 1 1755 ZG Petten INH) The Netherlands Telephone (0)2246 - 6262 Telex 57211 ECN-87 SEPTEMBER 1980 DISPLACEMENT AND EXCHANGE REACTIONS IN RADIOANALYSIS BY P.C.A. OOMS Proefschrift Vrije Universiteit Amsterdam, 30 september I980 - J CONTENTS Page CHAPTER 1. INTRODUCTION 9 1.1. Classification of separation methods 10 1.7.1. Reaction with a free reagent 10 1.1.2. Displacement 11 1.1.3. Isotopic exchange 12 1.2. Analytical criteria 12 1.2.1. Activation analysis with a spe­ cific reagent 13 1.2.2. Isotope dilution analysis with a specific reagent 14 1.2.3. Activation analysis with a non­ specific reagent 14 1.2.4. Isotope dilution with a non-speci­ fic reagent 14 1.2.5. Isotopic exchange 14 1.3. Selection of procedures 15 1.3.1. Liquid-liquid extraction using a non-specific chelating agent 16 1.3.2. Amalgams 16 1.3.3. Loaded active carton 18 1.3.4. Coulometry 19 1.4. List of symbols 21 1.5. Summary of contents 23 1.6. References 25 CHAPTER 2. APPLICATION OF DISPLACMENT - AND EXCHANGE REACTIONS IN NEUTRON ACTIVATION AND ISOTOPE DILUTION ANALYSIS 27 2.1. Introduction 28 2.2. Calculations of equilibrium concentrations 28 2.2.1. Definitions 28 2.2.2. Theoretical considerations 29 - 6 - Page 2.2.3. Numerical calculations 31 2.2.3.!. Programmes 31 2.2.3.2. Precision of the calculated q-values 33 2.2.4. Application 34 2.2.4.1. Activation analysis 34 2.2.4.2. Isotope dilution analysis 34 2.3. Experimental 35 2.3.1. Chemicals and apparatus 35 2.3.2. Procedure 35 2.4. Conclusions 36 2.5. References 37 CHAPTER 3. RADIOMETRIC DETERMINATION OF THE EXTRACTION CONSTANTS OF SOME METAL DIETHYLDITHIOCARBAMATES IN THE SYSTEM CHLOROFORM/WATER 38 3.1. Introduction 39 3.2. Theory 40 3.3. Experimental 41 3.3.1. Chemicals and equipment 41 3.3.2. Procedure 42 3.4. Results 42 3.5. Discussion 45 3.6. References 47 CHAPTER 4 CALCULATIONS ON PARTITION EQUILIBRIA IN LT/^JID- LIQUID EXTRACTION SYSTEMS, APPLIED TO THE SEPARATION OF METAL IONS FROM AQUEOUS SOLUTIONS 48 4.1. Introduction 49 4.2. Theory 51 4.2.1. Definitions 51 4.2.2. Theoretical considerations 51 - 7 - Page 4.3. Calculations 54 4.3.1. Computer programmes 54 4.3.2. Applications in activation analysis 54 4.3.3. Application in isotope dilution analysis 55 4.4. References 56 CHAPTER 5. MULTIELEMENT ISOTOPE DILUTION ANALYSIS BY MEANS OF RADIOMETRIC TITRATION 71 5.1. Introduction 72 5.2. Principle 73 5.2.1. Definitions 73 5.2.2. Theoretical considerations 73 5.2.3. Optimization of the Kl -values 75 5.3. Experimental 76 5.3.1. Chemicals and equipment 76 5.3.2. The titration vessel 76 5.3.3. Procedure 78 5.4. Results 79 5.4.1. Experiments to check the apparatus 79 5.4.2. Radiometric titrations of some solutions of metal ions 81 5.4.2.1. Titration of a 3.2xl0~4 M Cu(II) solution with a 2 l.Oxlo" M Zn(DDC)2 solution in chloroform 81 5.4.2.2. Titration of a mixed solution of 3.15xl0~6 M Cu(II) and l.OxlO-1 M Pb(II) with 4 2.5xlO~ M Zn(DDC)2 dissolved in chloroform 81 5.5. References 84 CHAPTER 6. ISOTOPE DILUTION ELECTROANALYSIS 85 6.1. Introduction 86 6.2. Principle 86 6.2.1. Procedure I: two electrolytic cells connected in series 86 6.2.2. Procedure II: electroysis in one single cell 87 6.3. Experimental 88 6.3.1. Apparatus 88 6.3.2. Reagents 91 6.3.3. Procedures 91 6.4. Results 92 6.4.1. Results from Procedure I 92 6.4.2. Results from Procedure II 92 6.5. Discussion 93 6.6. References 93 APPENDIX I DESCRIPTION OF THE COMPUTER PROGRAMMES QFORW AND QPLOT 95 APPENDIX II TEXT OF THE COMPUTER PROGRAMMES QFORW AND QPLOT 111 APPENDIX III DESCRIPTION OF THE COMPUTER PROGRAMME QBACK 139 APPENDIX IV TEXT OF THE COMPUTER PROGRAMMA QBACK 147 APPENDIX V DESCRIPTION OF THE APPARATUS FOR SEMIAUTOMATIC LIQUID-LIQUID EXTRACTION 159 SAMENVATTING 163 CURRICULUM VITAE 1 - 9 - CHAPTER 1. INTRODUCTION SUMMARY The application of displacement and exchange reactions in radioanalysis is discussed. A few cases are selected for further investigation. The contents of the other chapters are suimarized. - 10 - 1.1. Classification of separation methods Many analytical procedures involve an isolation of the compound of inte­ rest effected by its transfer to another phase. Usually this implies dissolution of the sample. One might then summarize these determinations by the following scheme: sampling —• dissolution —> separation —•• measurement The separation procedures, based on reaction between the compound to be determined and a reagent, have been distinghuished into three types accor­ ding to the "reagents" which are used: a) reaction with a free reagent (section 1.1.1.) b) displacement reac­ tions (section 1.1.2.) c) isotopic exchange reactions (section 1.1.3.). From the point of view of radioanalysis one should make a second dis­ tinction by the amount of reagent which may be present in excess or in a substoichiometric quantity. Both situations are met in activation ana­ lysis. Isotope dilution methods are based on the addition of a sub­ stoichiometric amount of reagent. In this thesis attention will be restricted to one step separation pro­ cedures. 2i]>iJK_Reaction_with_a_free_reagent The reagent R may react with the compound C according to aR + C t R C (1) where a represents the stoichiometric ratio. An equilibrium constant is defined by equation (2) [RC] a = K (2) [Rf[C] eq Separations based on adsorption belong to this class, in that sense that a is no longer the stoichiometric ratio, but the (variable) ratio of the amount of adsorbent and the component to be adsorbed. Usually the product K [R] is very large and thus the recovery of C vir­ tually complete. Examples of this situation are found in the determina­ tion of mercury in air by adsorption to active carbon |l|, or Mn02 |2J, and that of trace elements in dry biological material by dissolution, - 11 - dilution and adsorption to active carbon |3|. Adsorption has not been applied in isotope dilution analysis since the reproducibility in taking substoichiometric amounts of the adsorbent in case of very low concentrations of the compound to be adsorbed is very poor. Electrodeposition belongs also to this type of reaction. It has been applied in activation analysis for the determination of |4|. The use of coulometry has been reported for the isotope dilution analysis of Cd |5|. lili^ J)is£lacement The reagent R is added as R A which is present in a separate phase. A h^s to be displaced by the analyte B; that is: |RQA + B i RgB + §A (3) Again one can define an equilibrium constant. [RHB][A]I 3 = K (4) I eq [R A]°[B] a There are many applications of displacement reactions in chemical sepa­ ration. A further classification may be brought about by defining the reagent phase. The most common case is addition of the reagent dissolved in an organic liquid, immiscible with the aqueous phase containing the element(s) to be determined. A survey of the procedures is given in ref. |6|. In radioanalysis this approach is used in activation analysis as well as in isotope dilution methods. In the latter case the reagent should be specific or the interferences should be removed first |7|. In activation analysis specificity is not imperative but it may be so if it is necessary to obtain a radiochemically pure counting aliquot or at least a convenient group separation. Another group of displacement reactions is based on ion-exchange. Again the applications in activation analysis are numerous. A survey may be found in refs. |8| and |9|. The use in isotope dilution has been restricted to the determination of a single species |10|. - 12 - A third class of displacement reactions is presented by the isomorphous exchange between an aqueous solution and a insoluble salt. The experi­ ments in this domain belong to the oldest part of radiochemistry |il, 12f. Applications in activation analysis have been reported for the lanthanides |13|. The possibility of separating manganese has been discussed [I4|. This principle cannot be used in isotope dilution. 1.1.3. Isotopic exchange The interest of this group of separations is restricted to analytical methods with the aid of which isotopes of a nuclide can be disting­ uished, i.e. radioanalysis and mass spectrometry. It is characterized by the reaction C + C* t C* + C (5) where the bar denotes the second phase and the asterisk the species with a particular isotopic composition. The equilibrium constant is about equal to unity. Small but distinct differences, known as the isotopic effect, may exist for light elements |l5|. The application of isotopic exchange in radioanalysis is mainly found in activation analysis. The isolation of iodine from irradiated rainwa­ ter may be cited |l6|. The exchange between an aqueous solution of a lanthanide and one of its insoluble salts, mentioned above, is another example. The interaction between an aqueous solution of a (heavy) metal ion and an amalgam presents a third type of exchange reactions |17|.
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