«‘4' )V1531;] RETURNING MATERIAL§: Place in book drop to LJBRARJES remove this checkout from _:-__ your record. FINES will ——~ be charged if book is returned after the date stamped below. _ H __-._-1..____. . _ __ . ‘ “ . 7:“QW.~;3 "“- ..... ---— ~ _._. NNR STUDIES OF THE KINETICS OF THE EXCHANGE REACTIONS OF THE LITHIUM, SODIUN, AND TEALLIUICIONS NITN ll-CRONN-G, 15-CRONN-5 AND PENTAGLYNE IN SOME NONAQUEOUS SOLUTIONS BY Yongsheng Hou A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1988 ABSTRACT NMR STUDIES OF THE KINETICS OF THE EXCHANGE REACTIONS OF THE LITHIUM, SODIUM, AND THALLIUM IONS WITH 18-CRONN-6, 15-CROWN-5 AND PENTAGLYME IN SOME NONAQUEOUS SOLUTIONS BY Yongsheng Hou Kinetic.studies of the exchange reactions of the metal ions between their uncomplexed and complexed sites by the crown ethers and the linear pentaglyme were carried out by dynamic NMR spectroscopy. For sodium tetraphenylborateWaBPha with the 18- Crown-6, the investigations have been performed in 1,2- dimethoxyethane(DME) solutions, as well as in binary mixtures of OMB and THF(tetrahydrofuran). The exchange mechanisms in all cases followed the so-called associative— dissociative process. The nearly linear dependence of the kinetic parameters on the composition of solvent mixtures was found. In pure DME solutions at 298° K, for the associative-dissociative exchange reactions, the decomplexation reaction rate constant k, = 8000:2000 s”, the activation energy E. = 4.5:0.2 kcal'mol", the activation enthalpy M!" = 3.7:0.2 kcal'mol", the activation entropy AS‘ = -28.2i0.8 calmmflfhxd, and the activation free energy AG‘ = 12.1:0.1 kcal'mol“. In 3:1 DME:THF mixtures(molar), the results are: k.2 = 35001-800 s", Ell = 6.83:0.2 kcal‘mol", AH‘ = 5.21:0.2 kcai-mol", AS‘ = ~21.3:0.7 cal°mol"'l(", and A0‘ = 12.610.1 kcal'mol'1. In 1:1 DME:THF mixtures(molar), the results are: k.2 = 18001-300 s“, E, = 7.710.8 kcal'mol", AH‘ = 7.110.8 kcal'mol", AS‘ = —2011 cal'mol"'K", and AG" = 13.0104 kcal'mol". Thermodynamic studies of the complexation reactions of NaBPh, and NaSCN(sodium thiocyanate) with the 18C6 in ONE ‘solutions show that the formation constants for the complexes of these two salts are log K,:- 3.9510.06 and 2.810.2 respectively. Kinetic parameters of the exchange reactions were also measured for the systems of lithium perchlorate with 15- Crown-S in acetonitrile and nitromethane solutions. It was found that the exchange reaction for the lithium ion proceeds by the associative-dissociative mechanism in acetonitrile(AN) solutions while in nitromethane(NM) solutions the exchange goes by the bimolecular pathway. In AN solutions, x, =- 25001400 s", E, - 4.3310,01 kcal'mol", An‘ - 4.2410.01 kcal'mol", As‘ =- -24.3:0.3 cal'mol"'K", and AG‘ - 114510.09 kcal'mol"; for the bimolecular exchange in NM, 1:, = 150000140000 s‘1-M", E, = 4.9810.09 kcal'mol", AH‘ = 4.3910.09 kcal'mol“, as‘ = -20.110.2 cal'mol'1'K", and A6‘ = 10.410.2 kcal'mol". In AN solutions, the Tl‘oion exchange in the TlClO, + 18C6 system proceeds by the bimolecular pathway; the associative-dissociative and the bimolecular processes both exist for the T1C10, + pentaglyme(PG) system. In the first case, 1:, = (4.11-0.2)x107 3'1'M“, Ell = '2 kcal'mol", AH‘ = ”1.4 kcal'mol", As‘ = ‘-19 cal-mo1'1-K", and AG‘ = 7.0610.03 l-ccal°mol'1 at 298° K. In the second case, for the bimolecular mechanism the results are: k, = (3.110.1)x108 s"'M", E. = . 3.0010.05 kcal'mol'1, AH‘ = 2.4110.05 kca1°mo1", AS‘ = -11.610.2 cal-moi“-K", and A6‘ = 5.3810.02 Real-moi": for the associative-dissociative mechanism, the results are: k.2 = (2.210.4)x105 s“, E. = ~5 kcal'mol“, AH‘ = '4 kcal'mol", AS‘ = "-19 cal'mo1'1'K", and AG" =- 10.2-10.1 kcal'mol". To My Mother ACKNOWLEDGEMENT The author wishes to thank Dr. Alexander I. Popov for his patient guidance and warm encouragement, without which the completion of my study at Michigan State University would not be possible. The author is also indebted to the NMR group for their technical help and their enthusiastic maintenance of NMR facilities. Sincere gratitude is extended to Dr. T.V. Atkinson for his work to ease problems concerning computer applications involved in this work. Last, but not the least, the author would like to express his greatest appreciations that no words can describe to his mother and brother, and to all his relatives and friends for their loving, caring, and supporting throughout the whole course while he was pursuing his degree. vi Table of Contents Chapter Page List of Tables . . . . . . . . . . . . . . . . . . . . iv List of Figures . . . . . . . . . . . . . . . . . . . . ix Chapter 1 HISTORICAL REVIEW . . . . . . . . . . . .1 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . 2 1.2 THERMODYNAMIC AND KINETIC STUDIES . . . . . . . . 4 1.2.1 The influence of ligand properties on the complexation kinetics . . . . . . . . . . . 10 1.2.2 The role of cations in complexation kinetics O O O O O O O O O O O O O O O O O O 18 1.2.3 The influences of solvent properties on the kinetics of the complexation and the exchange reactions . . . . . . . . . . . . . . . . . 23 1.3 PURPOSES OF THIS STUDY . . . . . . . . . . . . . 33 Chapter 2 EXPERIMENTAL SECTION . . . . . . . . . . . . . 44 2.1 Purifications of solvents and salts . . . . . . . 45 2.2 Dynamic NMR spectroscopy . . . . . . . . . . . . 46 2.2.1 Concepts of dynamic NMR spectroscopy . . . . 46 2.2.2 Theoretical Aspects of Dynamic NMR Spectroscopy . . . . . . . . . . . . . . . . 51 2.2.2.1 In the absence of the exchange reactions . . . . . . . . . . . . . . . 51 2.2.2.2 In the presence of the exchange reactions . . . . . . . . . . . . . . . 55 2.3 Procedures of dynamic multi-NMR measurement . . . 64 vii Chapter Page 2.3.1 Multi-NMR measurement . . . . . . . . . . . 64 2.3.2 Temperature calibration of the probe for variable temperature studies . . . . . . . . 65 2.3.3 Data treatment . . . . . . . . . . . . . . . 66 Chapter 3 KINETIC STUDIES OF THE COMPLEXATION OF THE SODIUM ION BY 18C6 IN 1,2-DIMETHOXYETHANE AND MIXTURES 0F 1,2-DIMETHOXYETHANE AND TETRAHYDRAFURAN . . 71 3 O 1 INTRODUCTION O O O O O O O O O O O O O O O O O O 72 3.2 Results and Discussion . . . . . . . . . . . . . 73 3.2.1 Solvation and ion pair formation in DME and THE solutions . . . . . . . . . . . . . . . . . 73 3.2.2 Thermodynamic studies of sodium salt complexes in 1,2-dimethoxyethane . . . . . . . . . . . 75 3.2.3 Molecular dynamic studies of the free sodium salts and their complexes by 18C6 . . . . . 76 3.2.4 Kinetic studies of the complexations of sodium salts and 18C6 . . . . . . . . . . . . . . . 80 3 O 3 CONCLUSION O O O O O O O O O O O O O O O O O O O 90 Chapter 4 KINETIC STUDIES OF THE EXCHANGE REACTION OF THE THALLIUM ION WITH 18C6 AND PENTAGLYME IN ACETONITRILE O O O O O O O O O O O O O O O O O 1 3 4 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . 135 4.2 RESULTS AND DISCUSSION . . . . . . . . . . . . 136 4.2.1 Molecular dynamics of the uncomplexed thallium ions and the complexed thallium ions by 18- Crown-6 and pentaglyme . . . . . . . . . . 136 4.2.2 Kinetic studies of the exchange reactions of TlClO, with 18C6 and pentaglyme in acetonitrile solution . . . . . . . . . . . . . . . . . 137 4 O 3 CONCmS IONS O O O O O O O O O O O O O O O O O O 148 Chapter 5 KINETIC STUDIES OF LITHIUM PERCHLORATE COMPLEX BY 15-CROWN-5 IN ACETONITRILE AND NITROMETHANE .169 5.1 INTRODUCTION . . . . . . . . . . . . . . . . . 170 Chapter Page 5.2 RESULTS AND DISCUSIONS . . . . . . . . . . . . 171 5.2.1 Molecular dynamics of the uncomplexed lithium perchlorate and the complexed lithium perchlorate by 15C5 in acetonitrile and nitromethane solutions . . . . . . . . . . 171 5.2.2 The kinetics of the exchange reactions of lithium salts in acetonitrile and nitromethane solutions . . . . . . . . . . . . . . . . 172 5.3 CONCLUSION . . . . . . . . . . . . . . . . . . 181 Appendix A DATA TRANSFER . . . . . . . . . . . . . . . .199 Appendix B GETNMR.FOR . . . . . . . . . . . . . . . . .201 Appendix C Data Transformation . . . . . . . . . . . . .204 Appendix D NIC180--Data formatting programs . . . . . .205 Appendix E EXAMPLES OF DATA FILES . . . . . . . . . . .213 E.l TEST.DAT . . . . . . . . . . . . . . . . . . . 214 E.2 TEST.KIN . . . . . . . . . . . . . . . . . . . 215 E.3 TESTK.DAT . . . . . . . . . . . . . . . . . . . 218 Appendix F Appendix G Appendix H Appendix I KINBLD O COM O O O O O O O O O O O O O O O O O 2 2 1 KINRUN O COM O O O O O O O O O O O O O O O O O 2 2 2 SUBROUTINE EQN-NMRZSITE.FOR . . . . . . . . .224 SUBROUTINE EQN-NMRISITE.FOR . . . . . . . . .230 Table List of Tables Page Ionic diameters of cations and diameters of cavities of crown ether molecules(A) . . . . . . . . . . . 38 The stability constants of 18C6- and pentaglyme- metal complexes . . . . . . . . . . . . . . . . . 39 The complexation and decomplexation rate constants of some alkali and alkaline earth cation cryptates in methanol . . . . . . . . . . . . . . . . . . . 40 Complexation and decomplexation rate constants of lithium and cesium cryptates in various solvents .41 Rate constants of dissociation (kg), formation (kg), and formation constants (K1) for the cryptates Ag(C222)* and K(C222)’in acetonitrile + water mixtures at 25 (2 . . . . . . . . . . . .'. . . . 42 Physical Properties of 1,2-dimethoxyethane and Tetrahydrofuran as Function of Temperature . . . 92 The equivalence conductances of NaBPh, Salt and its complex with 18C6 in THF and DME at 28(: . . . . 93 Sodium-23 Chemical Shifts of DME Solutions Containing Sodium Tetraphenylborateb and 18C6 at Various Mole Ratios at Room Temperature . . . . . 94 Sodium-23 chemical shifts of DME solutions containing sodium thiocyanate’ and 18C6 at Various Mole Ratios at Room Temperature . . . . . . . . . 95 X Table 10 11 12 13 14 15 16 17 18 19 Page Sodium-23 relaxation rates and chemical shifts of the free NaBPh, and complexed NaBPh, by 18C6 in DME solution . . . . . . . . . . . . . . . . . . . . 96 Relaxation times and chemical shifts of 23Na of the free NaBPh‘ and complexed NaBPh, by 18C6 in the mixture of DMEzTHF (3:1, mole fraction) . . . . . 97 Relaxation times and chemical shifts of‘aNa of the free NaBPh, and complexed NaBPh, by 18C6 in the mixture of DME:THF (1:1, mole fraction) . . . . . 98 Sodium-23 relaxation times and chemical shifts of the free NaClO, and complexed NaClO, by 18C6 in DME solution . . . . . . . . . . . . . . . . . . . . 99 Sodium-23 relaxation times and chemical shifts of the free NaSCN and complexed NaSCN by 18C6 in DME solution . . . . . . . . . . . . . . . . . . . .100 The sodium ion mean lifetimes of NaBPh, with 18C6 in DME solution . . . . . . . . . . . . . . . . . .101 The sodium ion mean lifetimes of NaBPh, with 18C6 in the mixture of DME:THF (3:1, mole fraction) . . .104 The sodium ion mean lifetimes of NaBPh, with 18C6 in 1:1 (Mole fraction) DME:THF Solution . . . . . .105 The rate constants of the decomplexation of NaBPh 18C6 complex in 1,2-DME solution . . . . .106 The rate constants of the decomplexation of NaBPh(18C6 complex in DME:THF(3:1,mole fraction) mixture . . . . . . . . . . . . . . . . . . . . .107 xi Table 20 21 22 23 24 25 26 27 28 Page The rate constants of the decomplexation of NaBPhy18C6 complex in DME:THF(1:1,mole fraction) mixture . . . . . . . . . . . . . . . . . . . . .108 Kinetic parameters of the decomplexation of NaBPhp-18C6 complex in THE, 1,2-DME and the mixtures of THF and 1,2-DME at 298 K . . . . . . . . . . .109 The comparison of the experimentally determined kinetic parameters to those calculated . . . . .110 The comparison of the chemical shifts and the relaxation times of NaBph, and NaBPh‘ Complex with 18C6 in THF, 1,2—DME and the mixture solutions .111 A list of some physicochemical properties of some metal ions . . . . . . . . . . . . . . . . . . .149 Comparison of the complexations of thallium and potassium . . . . . . . . . . . . . . . . . . . .150 Tl-205 chemical shift and relaxation time of the free thallium perchlorate(0.01M) in acetonitrile . . . . . . . . . . . . . . . . . .151 Tl-205 chemical shift and relaxation time of the complexed thallium perchlorate(0.01M) by 18C6 in acetonitrile . . . . . . . .7. . . . . . . . . .152 Tl-205 chemical shift and relaxation time of the complexed thallium perchlorate(0.01M) by pentaglyme in acetonitrile . . . . . . . . . . . . . . . . .153 xii Table 29 30 31 32 33 34 35 Page The mean life times of the thallium ion in the system of TlClO‘ with 18C6 in acetonitrile solutions . . . . . . . . . . . . . . . . . . . .154 The mean life times of the thallium ion in the system of T1C10‘ with pentaglyme in acetonitrile . . . . . . . . . . . . . . . . . .155 The exchange rate constants(kq) of the thallium ion in the system of T1C10,, with pentaglyme in acetonitrile via the bimolecular exchange mechanism and the exchange or the decomplexation rate constant(kd or k.2) via the associative-dissociative mechanism, T1C10:0.01M . . . . . . . . . . . . .156 The exchange rate constants of the thallium ion in the system of TlClo, with 18C6 in acetonitrile, T1C10:0.01M..................157 The kinetic information of the exchange reactions of TlClO‘ in acetonitrile solutions with 18C6 and pentaglyme at 298k . . . . . . . . . . . . . . .158 Lithium-7 relaxation times and chemical shifts of the free LiClO, and complexed LiClO, by 15C5 in acetonitrile solutions . . . . . . . . . . . . .182 Lithium-7 relaxation times and chemical shifts of the free LiClO, and complexed LiClO, by 15C5 in nitromethane solutions . . . . . . . . . . . . .183 xiii Table 36 37 38 39 40 41 Page The lithium ion mean life times of LiClO‘ with 15C5 in acetonitrile solutions at different relative concentrations of the salt to the ligand . . . .184 The lithium ion mean life times of LiClO, with 15C5 in nitromethane solutions at different relative concentrations of the salt to the ligand . . . .185 The decomplexation rate constants of LiC10,, complex by 15C5 in acetonitrile solutions at different temperatures . . . . . . . . . . . . . . . . . .186 The exchange reaction rate constants of LiClo, complex by 15C5 in nitromethane solutions at different temperatures . . . . . . . . . . . . .187 The kinetic information of the exchange reactions of LiClO, in acetonitrile and nitromethane solutions when 15C5 is present at 298 K . . . . . . . . . .188 Complexations of some ligands with neutral organic molecules in benzene at 298 K . . . . . . . . . .189 xiv Figure List of Figures Page Structures of some synthetic and naturally occurring macrocyclic and linear ligands . . . . . . . . . 43 Na-23 chemical shift of NaBPh,.as a function of the concentration of 18C6 ligand in DME solution at 25C......................112 Na-23 chemical shift of NaSCN as a function of the concentration of 18C6 ligand in DME solution at 25C......................1l3 Na-23 chemical shifts of the uncomplexed NaBPh, and the complexed NaBPh‘ by 18C6 as functions of temperature in DME . . . . . . . . . . . . . . .114 Na-23 chemical shifts of the uncomplexed NaBPh, and the complexed NaBPh, by 18C6 as functions of temperature in DME:THF(3:1,molar) mixture . . . .115 Na-23 chemical shifts of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of temperature in DME:THF(1:1,molar) mixture . . . .116 Na-23 chemical shifts of the uncomplexed NaClO‘ and the complexed NaClO, by 18C6 as functions of temperature in DME . . . . . . . . . . . . . . .117 XV Figure 10 11 12 13 14 15 16 Page Na-23 chemical shifts of the uncomplexed NaSCN and the complexed NaSCN by 18C6 as functions of temperature in DME . . . . . . . . . . . . . . .118 The relaxation rates of Na-23 of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of reciprocal temperature in DME . . . . . . . .119 The relaxation rates of Na—23 of the uncomplexed NaBPh, and the complexed NaBPh, by 18C6 as functions of reciprocal temperature in DME:THF(3:1, molar) mixture . . . . . . . . . . . . . . . . . . . . .120 The relaxation rates of Na-23 of the uncomplexed NaBPh‘ and the complexed NaBPh, by 18C6 as functions of reciprocal temperature in DME:THF(1:1, molar) mixture . . . . . . . . . . . . . . . . . . . . .121 The relaxation rates.of Na-23 of the uncomplexed NaClO, and the complexed NaClO, by 18C6 as functions of reciprocal temperature in DME . . . . . . . .122 The relaxation rates of Na-23 of the uncomplexed NaSCN and the complexed NaSCN by 18C6 as functions of reciprocal temperature in DME . . . . . . . .123 ln (l/r) against l/T for the system,NaBPh‘-+ 18C6 in DME solutions . . . . . . . . . . . . . . . . . .124 ln (1/1) against l/T for the system NaBPh,-+ 18C6 in DME:THF(3:1,molar) mixtures . . . . . . . . . . .125 ln (l/r) against 1/T for the system.NaBPh,-+ 18C6 in DME:THF(1:1,molar) mixtures . . . . . . . . . . .126 xvi Figure 17 18 19 20 21 22 23 24 25 26 27 Page 1/1[Na]t vs. 1/[Na‘], for NaBPhl, + 18C6 in DME solution . . . . . . . . . . . . . . . . . . . .127 1/r[Na], vs. 1/[Na‘], for NaBPh, + 18C6 in DME:THF(3:1,molar) mixture . . . . . . . . . . .128 1/r[Na], vs. 1/[Na‘], for NaBPh, + 18C6 in DME:THF(3:1,molar) mixture . . . . . . . . . . .129 The Arrhenius plot for the system of NaBPh,-+ 18C6 in the pure DME solution. In R vs. 1/T . . . .130 The Arrhenius plot for the system of NaBPh4-+ 18C6 in DME:THF(3:1, molar) mixture. ln k vs. l/T .131 The Arrhenius plot for the system of NaBPh,-+ 18C6 in DME:THF(1:1, molar) mixture. ln k vs. 1/T .132 Activation parameters as functions of the composition of the binary mixture of DMEzTHF . .133 Tl-205 chemical shifts of the uncomplexed TlClO, and the complexed TlClo‘ by 18C6 and pentaglyme ligands in acetonitrile solutions as functions of temperature . . . . . . . . . . . . . . . . . . .159 Tl-205 relaxation rates of the uncomplexed TlClO, and the complexed TlClO, by 18C6 and pentaglyme ligands in acetonitrile solutions as functions of temperature . . . . . . . . . . . . . . . . . . .160 1n (1/7) vs. 1/T for the system TlC10,-+ 18C6 in acetonitrile solution . . . . . . . . . . . . . .161 1n (1/1) vs. 1/T for the system T1C10,-+ pentaglyme in acetonitrile solution. . . . . . . . . . . . .162 xvii Figure Page 28 1/r[Tl*], vs. 1/[Tl‘], for the system TlClO, + 18C6 in acetonitrile solution at several temperatures . .163 29 1/r[TIU, vs. 1/[Tlfh for the system T1C10,-+ pentaglyme in acetonitrile solution at several temperatures . . . . . . . . . . . . . . . . . .165 30 ln 1:, vs. l/T for the system TlClo, + 18C6 in acetonitrile solution. . . . . . . . . . . . . .166 31 lxllq vs. 1/T for the bimolecular exchange mechanism in the system TlClo4 + pentaglyme in acetonitrile solution . . . . . . . . . . . . . . . . . . . .167 32 ln k4 vs. l/T for the associative-dissociative mechanism in the system TlClo,-+jpentaglyme in acetonitrile solution . . . . . . . . . . . . . .168 33 Li-7 chemical shifts of the uncomplexed LiClO, and the complexed LiClO, by 15C5 as functions of temperature in acetonitrile and nitromethane solutions . . . . . . . . . . . . . . . . . . . .190 34 The relaxation rates of Li-7 of the uncomplexed LiClO, and the complexed LiClO, by 15C5 as functions of the reciprocal temperature in acetonitrile and nitromethane solutions . . . . . . . . . . . . .191 35 1/1[Li’], vs. 1/[Li‘], for Liam, + 15C5 in acetonitrile solution . . . . . . . . . . . . . .192 36 1/r[Li*], vs. 1/[Li’]f for Liam, + 1505 in nitromethane solution . . . . . . . . . . . . . .193 xviii Figure 37 38 39 40 Page ln (l/r) against l/T for the system LiClO,-+ 15C5 in acetonitrile solutions . . . . . . . . . . . . .194 ln (1/1) against l/T for the system LiC104-+ 15C5 in nitromethane solutions . . . . . . . . . . . . .195 In kd against l/T for the system LiClO, + 15C5 in acetonitrile solutions . . . . . . . . . . . . .196 lJIlq against l/T for the system LiC104-+ 15C5 in nitromethane solutions . . . . . . . . . . . . .197 xix Chapter 1 HISTORICAL REVIEW 1.1 INTRODUCTION The discovery and successful synthesis of macrocyclic polyether compounds, generally referred to as crown ethers, by Pedersen and coworkers,“3 followed by that of macrobicyclic polyether cryptands, by Lehn and coworkers’"5 in 1960's, sparked tremendous research interest and activities around the world about complexing abilities of these compounds towards metal ions, especially the alkali metal ions. These compounds are also biologically important for that they resemble their naturally-occurring counterparts which selectively complex and transport alkali metal ions in biological systems. They thus provide very useful models to study the nature and mechanisms of the reactions between metal ions and the naturally occurring ionophores in biological systems. Thermodynamic and kinetic studies of the complexation reactions of metal ions with these synthetic macrocyclic polyether ligands can provide extremely important information about mechanisms of complexation reactions.""7 Immediately following the synthesis of crown ethers, their abilities to complex alkali cations have been extensively investigated.”9 The effect of macrocyclic compounds on the ionic permeability of artificial and natural membranes, and the selective transport of alkali metal ions have been studied."MS Crown ethers have also been recognized for their roles in utilizing alkali metal ions for a variety of uses in catalysis, analysis, preparative Chemistry, and drug research.“47 The structures of some typical macrocyclic compounds as well as of some linear polyether ligands are shown in Figure 1. The following nomenclature proposed by Pedersen1 and Lehn‘ for cryptands and crown ethers will be used throughout this thesis. For typical cryptands, three bridge chains between the two nitrogen atoms are composed of -CH5§§0- units(Figure 1). The nomenclature for cryptands is as follows: Glyn, where l, m, and g are the numbers of oxygen atoms in three corresponding chains. For example, C221 means that it is a cryptand which has two oxygen atoms on two of the chains, and one oxygen atom on the third one. For crown ethers, the "plane ring" structures are made up by the same unit as in cryptands. Usually, they are named as m-Crown-n, where m and n refer respectively to the total number of atoms in the chain and the number of oxygen atoms it contains. For example, 18-Crown-6(or 18C6 for short) means that this crown ether has eighteen atoms in the ring, and six of them are oxygen atoms. There are also crown ethers which contain other functional groups and atoms such as cyclohexane or benzene on the CHgnn-o unit, as well as sulfur and nitrogen atoms occasionally replacing some oxygen atoms in the ring. The nomenclature of this group of compounds(See Figure 1) is similar to those given above. In this chapter, some recent studies on thermodynamics and kinetics of complexation reactions between the macrocyclic and linear compounds as ligands and metal ions will be reviewed. The major emphasis in this review will be on kinetics of complexation reactions which is the primary interest of the author. 1.2 THERMODYNAMIC AND KINETIC STUDIES Although the main objective of this study is the kinetics of the complexations of macrocyclic ligands and linear ligands with metal ions, an introduction to some background knowledge in the thermodynamics of complexations is necessary, since kinetics and thermodynamics are in many ways inseparable. The complexation reactions between the donor atoms of crown ethers and metal ions are results of ion—dipole interactions.‘ Most importantly, the complexing selectivities of crown ethers for certain metal ions are due to the consonance between the sizes of macrocyclic cavities with those of metal ions(see Table 1 for the sizes). In general, the better their sizes match, the more stable is the complex. The same considerations also hold true for cryptands. Very early studies of macrocyclic complexes, however, have shown that many other factors, such as the nature of the solvents(the solvating ability and the dielectric constant) as well as the nature of anions and the cationic charge density also have a strong influence in stabilities of these complexes.1 Comparisons of stabilities of complexes formed by the polyoxa- and polyaza macrocyclic ligands with those of their linear analogues(Table 2) clearly show that closure of the macrocyclic ring increases stabilities of complexes by several orders of magnitude(the macrocyclic effect!). However, whether the enhanced stabilities of the macrocyclic ligand complexes over the linear ligand complexes is entropic or enthalpic in origin is still not clear. One should not be surprised to see how little kinetic information is available relative to abundant amount of thermodynamic information. Most of the kinetic data has been obtained by ultrasonic relaxation and NMR measurements, since the complexation rate constants are much too high to be measured by the fast-mixing methods.18 It should be noted that the complexation reactions are also often accompanied by other simultaneous reactions, such as ion-pair formations, dimerization of the ion pairs of metal salts in solutions of low dielectric constants, as well as conformational change of ligands. When polyether ligands are added to solutions containing metal ions, complexation reactions between the ligands and cations occur. In order to explain the very high formation rates frequently observed, the concept of the stepwise replacement of coordinated solvent molecules, together with appropriate changes in the conformation of the ligands has been proposed.19 Direct evidence of conformational changes in ligandsnx’prior to complex formation, has come from ultrasonic relaxation studies. The proposed and the observed mechanisms for the complexation reactions of metal ions with macrocyclic ligands can be summarized in the following general scheme using monovalent cations as examples: k', 01 —’ (22 (la) k'.1 k1 M“A' :2: 1f + A“ (1b) k4 k2 k3 k: M’+Cz Z M‘-"cz :3 me; .2 (near (1c) k.2 k.3 k.‘ where M“AC and.MF are the ion pair and the free metal ion respectively, C1 and C2 are the two conformations of the ligands, while M‘mcz, M*'C2 and (MC)* are the three forms the complex representing the initial interaction between the metal ion and the ligand, the intermediate stage of the complex and the final wrapped form of the complex respectively. This reaction scheme postulates the existence of several equilibria prior to the final rate-determining steps of the complexation, which involves an initial conformational change of a ligand and/or desolvation of both the cation and the ligand, before the final form of the complex is formed. The following two mechanisms are called Eigen- Winkler‘9'26 and Chock's21 complexation mechanisms and have been observed operative in different situations. They are related to the mechanism given in Equation 1, from which they can be derived: Eigen-Winkler k, k2 k3 M" + c —".__ M*---c —"._ w-c : (MC)’(2) k-1 k-2 k-3 and Chock's k1 C1 +——- C2 (3a) k4 k2 w +c2 -', (near (3b). In Eigen-Winkler mechanism, the third step, which is the rearrangement of the ligand around the cation is considered to be the rate-determining step. This mechanism is equivalent to the previous mechanism but omits the step for the conformational change of the ligand. In Chock's mechanism the complexation step(the second step) is considered to be the rate-determining one and it can be obtained by neglecting the rearrangement steps of the ligand around the cation in the previous mechanism. These mechanisms have been investigated and discussed in several publications . 20.22-26 Usually, the complexation rates are high(reaching the diffusion controlled range)32 and can be explained by the assumption that the formation of a complex is a step-wise process so that the desolvation of the metal ions is largely compensated for by interaction with the ligand in the transition state and the activation energy reaches a minimum:32 It is clear that at this stage there is still no specific interaction between the ligands and the cations which would strongly differentiate between the various cations. Molecular models show that the oxygen atoms in the bridges can rotate outward from the cavity of a macrocyclic ligand, and these may form the basis of the initial interaction between the cations and the ligands. The subsequent steps in which the metal ion enters the cavity of the ligand, where the more specific size-dependent interactions occur, must then proceed rapidly from this stage. This mechanism strongly suggests that the transition state for the complexation reaction lies very close to the reactants. If, at equilibrium, the amount of a metal ion is in excess of that of the ligand, the cation will undergo an exchange between the free and the complexed sites. The exchange can proceed by one of two mechanisms, the bimolecular (I) and associative-dissociative (II) pathways proposed by Lehn et al."’and developed by Shchori et al.”: k1 (I) *M” + ML+ —-’, "ML+ + 11* (4a) R1 or kn kn "M+ + ML’ "“’._ *M*---L--- “"’._ *MU + M" (4b) kn kn k2 (II) M" + L _'l ML’ (5a) R2 or k21 k22 M" + L —' W"'L -—', ML” (5b) 5' 3 3' 5 In the bimolecular exchange mechanism, the uncomplexed and the complexed metal ions exchange between their sites in such a way that in the transition state both cations are simultaneously involved with the ligand. In associative- dissociative exchange mechanism, the same metal ion 10 exchanges between its complexed and uncomplexed sites and only one metal ion is present at the transition state. As in the thermodynamics of complexation reactions, ligands, cations, solvents, and anions all play important roles in influencing the complexation reaction kinetics. In general, dissociation rates have been shown to be much more sensitive than the formation rates to the variation in the ligand, cation and solvent.:‘-""3z'58 1.2.1 The influence of ligand properties on the complexation kinetics Ligands, as one of the two immediate participants of the complexation reactions, have direct influence on thermodynamics and kinetics of these reactions in many ways. The most striking influence of ligand structure on the kinetic behavior may be seen in the dissociation rates while formation rates do not correlate in any simple way with ligand structure(see Table 3) .3‘"9'58 For instance, the selectivity for a given cation vis-a-vis ligands is primarily determined by the dissociation rates(see Table 3).:32 The type(see Figure 1) of ligands, linear or cyclic, bicyclic(cryptands) or monocyclic(crown ethers), functional groups introduced into the ligands, and charged or ionizable ligands, all have influences on the complexation reactions. For a given cation , the complexation rate should depend upon the ability of the ligand to substitute, in a 11 stepwise manner, all or some solvent molecules of the inner coordination sphere of the cation by its coordinating sitesd” This ability should depend primarily on the flexibility of the ligands, but may also be influenced by the solvation of the ligands. From this point of view, more flexible ligands can interact more readily with the incoming cation, leading to more effective compensation for the loss of solvation energy. Usually, the more flexible crown ethers show faster complexation rates than the less flexible cryptands . 2°'32'58 The more flexible ligands also show faster dissociation rates for the complexes so that overall exchange rates are rapid. Cox et al.:33 investigated complexation kinetics of dibenzo—lB-Crown-6 with the strontium ion in methanol solutions at -15 °C by stopped flow technique and found that, as compared to cryptands, the more flexible crown ether ligand shows faster dissociation rate. The dissociation rate of Sr(Crown)”((2.710.3)x10 s4)is about 108 times faster than that of Sr(c222)2*(6.8x10’9 s") , while the formation rate constants for the two complexes are very similar((9.6i-0.5)x10” and 511 M'1s'1 for Sr(Crown)2+ and Sr(C222)”’respectively). The stability constant for the complex Sr(C222)2*(K,=7.9x10‘2 M") is correspondingly higher than that of Sr(Crown)2*(K,=3.6x103 M") . Thus, although the particular bicyclic structure of C222 does not appear in this case to strongly influence the formation rates, it has 12 a dramatic effect on the dissociation rates and on the stability constants. Introduction of functional groups on the skeletons of macrocyclic rings can change the flexibility and consequently influence the complexation kinetics. Cox and £3 gig“ studied the stabilities, formation and dissociation rate constants of alkali metal complexes with C2322 and C28232 cryptands in propylene carbonate solutions. The authors found that the substitution of the central -CH§N§- group in C222 by a benzene ring makes the ligand less flexible, and reduces the cavity size. The benzene structure also decreases the electron density on the oxygen atoms of the ligand, and increases the "organic" character of the ligand. The combined effect of these changes is the reduction in the stability constants of C2322 and €2,232 cryptates, relative to those of the unsubstituted cryptates and on the increase of the dissociation rates of the complexes. For example, the formation constants of Rb(C222)’, Rb(C2322)’ and Rb(c2,232)* are (1.04710.002)x109, (3.89010.003)x107,.and (4.26610.003)x106M"1 respectively, while the dissociation rate constants of the same complexes are (1.710.1)x10*, 3.310.2, and (1.8810.09)x10 s4. Open chain polyethers and macrocyclic polyether ligands form complexes with metal ions with substantial differences in the stabilities of the resulting complexes, i.e. the "macrocyclic effect" discussed previously(page 5). 13 Stabilities of complexes(measured by complex formation constants KF's) are directly related to the free energy change of the complexation reactions such that: RT 1n KF = "AG0 and 216° in turn is related to both the entropy change and enthalpy change of the reactions, i.e. AG° = AH° - TAS°. A negative change in AH° and a positive change in AS° both contribute to the stabilities of complexes. Kodama and et al.35'3‘7 studied equilibria and kinetics of complex formation between copper(II), zinc(II), lead(II), and cadmium(II) ions, and 12-, 13-, 14-, and 15-membered macrocyclic tetraamines(see Figure 1). In their studies, the authors have attempted to interpret the macrocyclic effect in terms of both thermodynamics and kinetics. These complexes show apparent macrocyclic effects and the formation constants of the macrocyclic complexes are several orders of magnitude larger than those for their linear analogues. The elevated stabilities of the macrocyclic complexes are the results of the favorable change of the entropy, with the enthalpy change having a slightly negative contribution(AH° is less negative for the cyclic ligands than the linear ligands). The authors argued that the 14 favorable entropy term is due to the favorable orientation of the macrocyclic ligands prior to chelation, and also due to the decreased macrocyclic complex solvation, as compared to that of linear complexes, in the inner coordination sphere as well as in the outer sphere because of the distorted geometry and the hydrophobic exterior of the ligands. The lower heat of formation of the cyclic complex may be attributed to several factors such as: the higher rigidity, and less coordinate bond energy in the change from two primary and two secondary to four secondary nitrogen atoms,(both with positive AHP'terms), and less ligand solvation (a negative AH° term). The comparison of the calculated dissociation rate constants indicates that the macrocyclic effect occurs most notably in the dissociation step. It was concluded in their study that the thermodynamic macrocyclic effect reflects more the dissociation rather than the formation process. It should be mentioned that protonation of the ligands dramatically retards the dissociation as well as the formation rate of the cyclic complexes. The authors also proposed that for the reaction of non-cyclic polyamine ligands, the kinetics are well explained by a dissociative mechanism which involves the desolvation of metal ions followed by the rate-determining step of the complexation-the first coordination bond formation: for a macrocyclic ligand, the reaction is likely to proceed by a concerted process of the desolvation and 15 metal-ligand bond formation because of the restricted geometry and the proximity of the N donors. In contrast to the macrocyclic effect observed in Kodama and coworkers study are those which seem to arise entirely or partially from the enthalpy term. Hinz and “‘39 assume that a lob-fold increase in the Margerum, stability constant of Ni(cyclam)”, as compared to Ni(2,3,2— tet)”, is due to a more favorable change in enthalpy which overcomes a less favorable change in entropy(cyclam: 1,4,8,1l-tetraazacyclotetradecane; 2,3,2-tet: N,N'-bis(2- aminoethyl)-1,3-prrpanediamine, also see Figure 1 for structures). They reasoned that the free macrocycle is less solvated than their linear counterparts due to steric hindrance and hence less enthalpic energy need be expended for desolvation before complexation. The cyclization of the ligands also contributes to the enhanced strength of the metal-nitrogen bond and leads to the favorable enthalpy change. The difference in ligands can also cause differences in the mechanism of the interactions of ligands with metal ions. Degani"0 studied kinetics of monensin(see Figure 1) complexation with sodium ions by 23'Na NMR spectroscopy and the results were compared to those of valinomycin(see Figure 1) and dicyclo-lS-crown-6(DCC). In going from MonNa to ValNaf'the association rate constants for all three complexes differ by about one order of magnitude, while the 16 dissociation rate constants differ by several orders of magnitude. The specificity of monensin for the sodium ion is thus mainly reflected in the slow dissociation rate of this complex. In observing the change in the entropies of activations, it can be seen that a very small decrease in entropy occurs when the activated sodium-monensin complex is formed from the free species. In contrast, the formation of the DCC-Na+ complex is accompanied by an appreciable negative activation entropy. This difference in the association activation entropies of the two complexes indicates that the crown ether conformation is most likely altered before the association with the sodium ion occurs, while the monensin anion does not undergo a conformational change prior to interaction with the sodium ion. The increase in entropy which occurs while going from the activated state to the complex is similar for both complexes, suggesting that a conformational change occurs after the sodium ion has interacted with the ionophore as has been shown to occur in Val-sodium complexation process."1 The conformational change of a crown ether prior to the association with a metal ion has also been observed for dicyclo-30-crown-10 by Chock and coworkers.21 Ionizable crown ethers(See Figure 1) represent another group of macrocyclic compounds, consisting of a polyether cavity and a proton ionizable group, which are capable of complexing cations with varying degrees of stability. Kinetically, complexations of alkali metal cations by 17 neutral crown ethers are very fast, approaching the diffusion-controlled limit of 108-109 M" s“.’°2 Again, a stepwise substitution of solvent molecules surrounding the ions, rather than a concerted process, has to be proposed to account for the high rates obtained.“3 It is expected that a negatively charged crown ether has a complexation rate as high as, or possibly even higher, than that for a neutral crown ether ligand. Actually, diffusion-controlled rates of formation for complexations of Nafiby the negatively charged antibiotics nigericin(2x1010 M”.s”) and monensin(1.1x109 M".s'1 ) have been found.L“'The formation rate constant of one order of magnitude faster for the Na*-+ nigericin reaction than that for the Na+ + monensin reaction indicates that there exists a direct interaction between the metal ion and the carboxylate group in nigericin but not between the metal ion and monensin in which the complex has a "zwitterionic" structure.‘5'“’ Eyring et al.""’8 studied sodium ion complexation by ionizable crown ethers in methanol-water solvent mixtures, and thermodynamics and kinetics of side- arm interaction were investigated. The authors found that the overall formation rate constants are in the range of diffusion-controlled reaction rates(“101o M”.s4). This formation rate is one order of magnitude greater than that for the Na*-+'monensin reaction and similar to that of the Na*-+ nigericin reaction. These results probably suggest 18 that the charged carboxylate side-arm interact with the cation to lower the energy barrier for the complexation. 1.2.2 The role of cations in complexation kinetics Cations, the other immediate participants of the complexation reactions, influence the reactions in very straight forward ways. The size-match of cations and ligands primarily determines the stabilities of the complexes and the selectivities of the complexations as discussed on page 4. As shown in the previous section(page 10), the selectivities are basically reflected in the dissociation rates of the complexes. Another one of the most important characters of cations that should be considered in these reactions are charge densities, which determine the abilities to be solvated by solvents and tendencies to form ion pairs. Most of such studies have dealt with the investigations of the complexations of alkali and alkaline earth ions. As the alkali and alkaline earth cations all have "noble gas" electronic configurations, the complexing properties of the ions depend primarily on their charge densities. The alkaline earth-metal complexes show much wider variations in stability reflected in the change of K, and both the formation(kq) and dissociation rates(ka) are smaller than those of the corresponding complexes of alkali metal cations of similar size.”9 19 For example, the formation rates of alkaline earth- metal cryptates are 101%“? times lower than those of the corresponding complexes of alkali metal ions of similar size(see Table 3):” It has been shown that the characteristic solvent substitution rate constants of the alkaline earth cations (except for Mg”) are extremely high (ca. 103-109 5‘1 in water) and are not very different from those of the alkali metal ions.“9 In terms of the Eigen- Winkler mechanisms, this means that during complexation ligands may not be able to substitute the solvent molecules in the alkaline earth ion solvation shell in a stepwise manner, and the energy required to achieve complexation is increased because there is no immediate compensation for the loss of solvation of the cation by the formation of cation- ligand bonds. As the result, any desolvation or partial desolvation required to reach the transition state in the complexation reaction should demand more energy if the cation is a strongly solvated Mb'than if it is a less solvated M‘. For the dissociation rate constants of the alkaline earth-metal complexes and the alkali-metal complexes, a difference of the order 102-105 5’1 is observed when comparing kd(MCry2*) with kd(MCry") .‘9 For the ligands studied, it has been found that in the alkaline earth family the formation rate constants of the complexes are in the order Ba2*‘>SrZ*’>Ca2+ (see Table 3):” This is the opposite order to that of the free energies of solvation of the cations. Thus, the energy barrier required 20 is lowest in the complexation process involving Ba”, larger for Sr”, and largest for Cab'which is the most strongly solvated of these three cations. A similar trend for the formation rate constants has also been observed for the alkali metal ions, but the differences in the values of k, from cation to cation, for a given ligand, are larger in the case of alkaline earth ions than in that of alkali ions.“‘9 The values of k, for Na+ and K+ complexes vary only by a factor of 2 or 3, whereas k, values for Baz“ cryptates are normally around 100 times higher than those for the Ca2+ cryptates. If the argument of solvation is used again, this difference is not unexpected, as the difference in free energy of solvation between Baa'and Ca2+ is much larger than that between K+ and Na*."9 The nature of the cations influences both the reaction rates and the exchange mechanisms. It seems that there is a trend of the change of the preference between the associative-dissociative and the bimolecular exchange mechanisms in the alkali metal family, from Nafl,IU to csfl5° The predominant exchange mechanism varies from that of either the associative-dissociative or bimolecular process for the uaf ion to primarily the bimolecular process for the Cs+ ion. Strasser et al.50 discussed their results of the exchange kinetics of the cesium ion with dibenzo-Zl-crown-7 and dibenzo-24-crown-8 in acetone and methanol solutions. In 21 all systems studied, the mechanisms of the exchange between the solvated and complexed Cs+ sites are predominantly the bimolecular process. A tendency to form more ion pairing or the decrease in charge density as one goes to the larger cation has been considered as the explanation of this trend, because ion pairing, or the decrease in charge density, actually minimizes the charge-charge repulsion in the bimolecular exchange mechanism and allows the bimolecular exchange mechanism to predominate. Shporer and et al.51 noticed the effect of the ionic strength of the solution on the rates of the reactions involving ionic species. Comparison of the results of experiments of D818C6 with the same sodium concentrations but with and without LiSCN present shows that in N,N- dimethylformamide the addition of the second salt slows down the rate of exchange. Since it has been shown that lithium ions do not compete effectively with sodium ions for the ligand, this observation were attributed to changes in activity and/or ion pairing. Conductivity measurements indicate that ion pair formation of metal salts in this solvent is not very large, and the effect of ionic strength on the rate constants, at least in this case, is due to changes of activities rather than to ion pairing. In terms of the transition-state theory, the observed rate constant is given by: kf = K‘ (kT/h) (YSMFYNaDBC/Y‘) 22 where K3 is the equilibrium constant for the formation of the activated complex, the y's are molar activity coefficients of the corresponding species and n is the number of solvent molecules involved in solvation of the cation. As can be seen, the change in solvent activity is one of the factors responsible for the decrease of kq‘with increasing electrolyte concentration. Replacement of the very bulky tetraphenylborate anion by the relatively small SCN' anion also leads to a considerable increase in the rate of the exchange. The very bulky tetraphenylborate anion may hinder the reorganization of solvent molecules in the vicinity of the sodium complex more effectively than the small SCN” ion, thus decreasing the activity of the solvent. It is clear that in some other cases ion pair formation does influence the complexation reaction kinetics to an important extent.52'53 NaBPh, + 18C6 system shows slow exchange in THF at room temperature and 42.27 kG, while under the same condition the exchange reactions are fast with other sodium salts such as NaSCN, NaI and NaClop This observation most likely is due to the differences in the types of ion pairs formed in the solutions. It is believed that in tetrahydrofuran solutions NaBPh, forms solvent- separated ion pairs“"""55 whereas the other three sodium salts tend to form contact ion pairs.“’In the latter case the anions can compete with the ligand for the cation more effectively, which lowers the stability of the sodium complex and increases the exchange rates. 23 Further investigations of the kinetics of the exchange reactions showed that the ion pair formation can also explain the difference in exchange mechanisms for NaBPh4-1 18C6 and NaSCN + 18C6 systems in THF solutions.”’The associative-dissociative exchange mechanism prevails for NaBPh4-1 18C6 while for NaSCN + 18C6 the bimolecular exchange mechanism dominates. It seems that the difference in the exchange kinetics in these two systems is due to the difference in the types of ion-pair formed. Contact ion pairs Na*'SCN' in THF solutions effectively reduce the cation-cation repulsion at the transition state of the bimolecular exchange mechanism and lower the energy level of the transition state, NaBPh, only forms solvent-separated ion pairs and the exchange occurs by the associative- dissociative mechanism. 1.2.3 The influences of solvent properties on the kinetics of the complexation and the exchange reactions Thermodynamics and kinetics of complexation reactions are influenced by the solvating abilities of solvents since the complexation process involves partial or complete desolvation of the cations and of the ligands. Moreover, as shown above, complexation process is influenced by interionic association and, therefore by the dielectric constant of the medium. 24 The solvating abilities can be measured by the donor numbers of the solvents defined by Gutmannfl'as the negative change of the enthalpy in kcal mole'1 upon the complexation of the solvents with SbCls in dilute 1,2-dichloroethane solutions: 1,2-DCE Solvent + SbC15 > Solvent'SbCls, DN = -AH Higher DN's correspond to more negative -AH and better solvating abilities. Influences of solvents on the complexation reaction kinetics, like the influences of cations and ligands, are reflected much more in the dissociation rates than in the formation rates of the complexation reaction(see Table 4).!58 For example, the dissociation rates increase sharply with increasing donor number of the solvent, covering a range of more than 9 orders of magnitude for the alkali ion cryptates, whereas the formation rates decrease but are much less sensitive to solvent variation. The significance of the solvent dependence of the formation and the dissociation rate constants of the complexation reactions is due to the fact that the properties of the transition state most closely resemble those of the reactants, therefore the transition state is closer to the reactants. The structures of the transition states can be identified from the differences of the 25 activation parameters of the complexation reactions. Shamsipur et al.“’studied the kinetics of the complexation reaction of Cs+ + C221 and Cs*-+ C222 systems in dimethylformamide solutions. The activation enthalpy, the activation free energy, and especially the activation entropy are quite different for the two different ligands. These differences arise mainly from the difference in the transition-state structure. Based on the positive entropy change for the release of Cs+ from the complex with C222 in DMF, it has been suggestedw’that the transition state for the release of the cation resembles the final state of the solvated Cs+ ion and cryptand. Although the change in activation energy with solvents for the Cs“C221 complex also requires the resemblance of the transition state to the final states of the solvated cation and the cryptand, negative activation entropy value for the decomplexation step implies the more rigid transition state for C221 than for C222. Differences in solvations of both cations and ligands in different solvents can readily explain the variation of the stabilities as well as the formation and the dissociation rate constants with solvents. As mentioned before, the complexation rates depend on solvations of cations in the inner coordination sphere and solvations of the ligandsd” The stability constants and the rates of formation and dissociation of complexes of the alkaline earth-metal cations Ca”, Sr”; and Bab'with cryptands C211, 26 C221, C222, C2322, and €2,232 have been measured in methanol solutions by Cox et al..‘69 The authors examined the solvent's influence on the complexation kinetics by comparing the results to those obtained in aqueous solutions. The change of reaction environment from water to methanol has the effect of increasing the formation rates of the complexes and reducing their dissociation rates, the both being related to the higher stabilities of the complexes in methanol compared to in water. Higher complexation rates in methanol are very probably due to weaker solvation of the free cation, and in cases like C222, also to weaker solvation of the ligand. However, the authors stated that ligands such as C2322 and C23232 are more strongly solvated in methanol than in water because of the more organic nature of these two cryptands than that of C222. This stronger solvation of the monobenzo and dibenzo ligands in methanol should contribute to lowering the values of formation rate constants k}, and in the case of Ca(C23232)2+ k, is extremely low(5 x 102 M"s") . For the alkali cryptates, the stronger solvation of ligands in water than in methanol was also proposed to explain the faster formation and the slower dissociation rates of cryptates in methanol solutionsf"2 The large increase in the stability of the cryptates on transfer from water to methanol supports assumption that the free cryptands are considerably more 27 strongly solvated in aqueous solution than in nonaqueous solvents. However, certain specific interactions between ligands and solvents and between ligands and cations can make exceptions to the generally observed solvent dependence of the complexation and the decomplexation reaction rate constants in terms of the solvating power of solvents.‘60 For example, the formation rates in water are much lower, and the dissociation rates much higher than expected because of the H-bonded interactions between water and the electronegative atoms, such as 0 and N, of the ligands. This specific interactions of water with the ligand is the explanation for the unusual kinetic behavior for the cryptate K(C222)+ in acetonitrile + water mixtures at 25 °C.‘° Both kd and k, have similar contributions to the increase of the stability constant of the complex with increasing mole fraction of acetonitrile due to the specific interactions of water with both the free cryptand and the resulting cryptate(see Table 5). In mixtures of acetonitrile + water the properties of the transition state cannot be closely related to those of either the reactants or the product. In the case of the cryptate Ag(C222)+ in acetonitrile + water mixtures at 25 °C, the dissociation rate constant, kg, of the complex shows a quite different dependence on solvent composition(see Table 5).‘60 The decomplexation rate constant is almost independent of solvent composition and the rapid decrease of the stability 28 constant with X“ near X“ = 0 is determined entirely by the variation in the formation rate constant due to the preferential solvation of the Ag‘ ion by acetonitrile. The independence of kg for the Ag(C222)+ complex in the mixtures indicates that in the transition state the silver ion is strongly bonded to the C222 nitrogen lone pairs in a way typical of the partially covalent interaction of monovalent d1o ions with nitrogen donors, therefore the strong preferential solvation by acetonitrile of the free silver is lost in the transition state and its properties resemble those of the fully complexed silver in the product state. Not only can the solvating power towards cations largely influence formation and especially decomplexation rates of complexation reactions, but it also affects the number of steps involved in complexation reactions.“1 For Na+ + 18C6 and Li*-+ 18C6 systems, it appears that the Eigen- Winkler multistep mechanism is operative, the number of steps during the complexation between the cation and 18C6 depends on the nature of the cation and the solvent. In ethanol, the uaf ion reacts with 18C6 in a single step but in DMF the reaction involves two steps. It may be that the desolvation step in DMF has a larger energy barrier so that it shows itself as a separate relaxation process while in ethanol solution the desolvation and the complexation are probably of equal rates within the resolution of the time scale of the experimental method. For the Li*-+ 18C6 system, the cation reacts with the ligand by a two-step process in 29 ethanol but only by a one-step process in DMF, an opposite situation of the Na*-+ 18C6 case. It is likely that the greater desolvation energy and ligand rearrangement involved in complexing Id? with respect to Na+ force the appearance of a two-step process in ethanol. The first step is an encounter process with a partial desolvation and ligand rearrangement and the second step is the complete encapsulation of the small Id? ion in the oversized 18C6 cavity, forcing the ligand to wrap around cation. In DMF, the last process involving the elimination of the coordinating solvent around Idf by 18C6, cannot occur to a significant extent due to the greater solvation of Id? than that of Na? in this solution. The above results demonstrate the importance of the solvent in determining the number of steps in the complexation process. The solvation of cations can also make the complexation reaction kinetics of crown ether-complexes different from those of cryptates, especially in the formation rate constants. The formation rate constants are much slower for cryptates than for the crown ether-complexes:63 One of the explanations for this behavior is the incomplete compensation for the loss of solvation of cations, because of the difficulties that cryptands have in adopting optimal conformations at various stages of complexation. The other explanation for the slower formation rates of cryptates than the crown ether-complexes is that in the multistep process of cryptate formation, there is a rate-determining step in 30 which two or more remaining solvent molecules of a partially complexed cation have to be removed prior to entry of the cation into the ligand cavity.‘62 To summarize, lower rates should occur for higher charge density cations and for solvents in which cation-solvent interactions are particularly strong, as well as for more rigid ligands which cannot effectively compensate for the loss of the solvation of cations by complexation.63 Solvents also play an important role in determining the exchange reaction mechanism. Shamsipur et a1.“ studied the exchange reaction kinetics of Cs? ion with DB30C10 in nitromethane, acetonitrile, propylene carbonate, and methanol solutions by'tBCs NMR. It was seen that in nitromethane solutions the dissociative exchange mechanism is predominant at all temperature studied, while in the other three solvents, the exchange is bimolecular below -10 °C; in propylene carbonate and methanol solutions above -10 °C the exchange follows the dissociative pathway. In the bimolecular exchange mechanism, the conformational rearrangement of the ligand must favor in the transition state a simultaneous departure of the complexed cation and an arrival of the new cation. Apparently, solvents with strong solvating ability help reduce the cation-cation repulsion in the transition state in the bimolecular exchange mechanism, while in solvents of poor solvating power the associative-dissociative mechanism is favored. At higher temperature, even in the good solvating solvents, the 31 associative-dissociative mechanism becomes predominant since the solvation ability of a solvent decreases with increasing temperature. The influences of solvents on the complexation reaction kinetics are also reflected in the activation parameters, such as activation energies, activation entropies and activation free energies, of the transition states of the reactions. The positive entropy of activation indicates solvent participation in the transition state.‘68 Usually, the high activation enthalpies correspond to weak solvation in the transition state and the net energy required to transfer NF cation from the complexed state to the solvent(uncomplexed M’) decreases with increasing solvent donicity which is a good measure of the solvation energy. For example, in the complexation kinetic study of K7-+ 18C6 in dioxolane and in a acetone-dioxolane mixture(80:20,v/v), the activation enthalpy values for the exchange reactions are 16.210.3 and 13.210.5 kcal mol'1 respectively, while in acetone solutions it is 8.610.5 kcal mol".‘65 Bhattacharyya et al.“’have shown that the large alkali cations remain practically unsolvated in tetrahydrofuran solutions. It is expected that the same lack of solvation would be observed in 1,2-dioxolane. Cahen et al.“’showed that the activation energies for the release of the Id? ion from Idf-C211 complexes in pyridine, water, dimethyl sulfoxide, dimethylformamide, and formamide increase with the increasing donicity of the solvents. The fact that the 32 activation energy for the release of the lithium ion from the cryptate complex increases with solvent donicity, opposite to the overall energy change between the initial and the final states for the decomplexation, indicates that the transition state must involve substantial ionic solvation. Shamsipur et al.“'also reported a similar trend of the change of the dissociation rates as well as activation energy and free activation energy with the change of the donicity of solvents. In other studies, the influence of solvent donicity on complexation kinetics was not observed. Ceraso et al."’8 found that in THF, H53, pyridine solutions the activation energy for the release of both sodium and lithium ions are not related to solvent donicity. Shchori et al.””” showed that the activation energies of the decomplexation of some Na(Crown)*‘complexes are independent of solvents, although the three solvents that they chosen in their study (methanol, dimethylformamide, and dimethoxyethane) coincidently have similar donicities--DN,,,O,,=25.7, DNDHF=26.6, and DNone=24 . It should also be noted that in complexation kinetic studies of metal ions with macrocyclic ligands, it is not uncommon that activation entropy(AS°) and enthalpy(AH°) of the decomplexation reactions compensate each other(AG° = M!" - TAS°) , so that the free activation energy somewhat 33 insensitive to solvents, and exchange rates vary by only a small factor.“'65'7° 1.3 PURPOSES OF THIS STUDY As described previously, kinetic data are relatively meager as compared to widely investigated thermodynamics of complexation , 8'15'71'73 even though they are equally important for the understanding of the selective transport process of cations by crown ethers or catalysis in reactions involving ionic species.” More studies about kinetics of the complexation in terms of the influences of solvents, ligands, cations and their counter ions on complexation kinetics are necessary to enlarge our present understandings of this field. Recent studies have reveal some interesting aspects of the kinetics of the complexation and the exchange reactions. The dependence of the exchange mechanism on temperature and on concentration was observed in studies by Popov et al..“”5 and by Detellier et al{“, respectively. The exchange reaction takes different pathways between the associative- dissociative and bimolecular processes at different temperatures in the same solutions or changes with the concentration of cations. The change of the activation energy with temperature was also observed. These observations are still not fully understood and further investigations are necessary. 34 The multistep complexation reaction mechanism proposed by Petrucci and Winkler‘9'20'22'26 emphasizes, in the complexation reactions, the influence of solvation of ligands and cations, of conformation change of ligands, and of the ion pair formation. The ion pair formations of electrolytes and aggregations of the ion pairs are determined by the dielectric constants of solvents. Dimethoxyethane and tetrahydrofuran have almost the same dielectric constants(7.20 and 7.39 at 25 °C respectively) but different solvating abilities towards cations.“’since in these two solvents the extent of ion pair formations should be approximately the same, they provide a fine opportunity to isolate the effects of the ion pair formation from that of solvation on the complexation kinetics. It has been postulated that in THF solutions there is a relationship between the types of the ion pairs formed and the exchange reaction kinetics.”’In the case of NaBPh4:h31 pairs are solvent-separated, while for NaSCN, NaI and NaClO, the contact ion pairs are formed. At room temperature on the NMR time scale of a spectrometer operating at 42.27 kG, the exchange reaction is slow for NaBPh, and fast for the other sodium salts between their uncomplexed sites and complexed sites by 18C6 ligand. For NaSCN, the charge-charge repulsion at the transition state of the bimolecular exchange mechanism is supposedly reduced by the contact ion pairs formed and the bimolecular exchange mechanism therefore prevails and the exchange reaction is fast. In the THF 35 solutions of NaBPh,, since the majority of the electrolyte forms solvent-separated ion pairs, the exchange reaction has to proceed by the associative-dissociative pathway and the reaction rates are relatively slow. Since DME has almost the same dielectric constant as that of THF, any differences in the exchange kinetics will reveal the difference of the two solvents in terms of the solvations. In addition, the kinetic investigation of the exchange reactions in DME solutions can serve as a probe to test the postulate of the influence of the ion pair formations on the exchange reaction kinetics. As pointed out by Strasser,“’kinetic studies of the exchange reactions involving lithium ions and crown ethers are essential to the full understanding of the influence of cations on the exchange reaction kinetics. Two mechanisms(the associative—dissociative and the bimolecular, Equations 4 and 5 on page 9) for the exchange of metal ions between their uncomplexed and the complexed sites. But which mechanism prevails depends on the factors such as ion pair formations, solvent donicities, and etc. Previous studies have shown that for the alkali metal ions with crown ethers there is a trend for the preference of the exchange pathways going from Na“ to K‘, and Cs‘. The predominant exchange mechanism for the Na+ ion is either the associative- dissociative or bimolecular process while the bimolecular process is primarily preferred for the Cs+ ion. Increased tendency to form ion pair due to the decreased charge 36 density as one goes to the larger cation has been considered as the explanation of this trend,“’because the charge- charge repulsion in the bimolecular exchange mechanism can be minimized by the ion paring and thus the bimolecular mechanism predominates. However, this conclusion has been based only on the kinetic studies of three of the five alkali cations and therefore is incomplete. The contribution of the of other alkali metal ions to the kinetic information is important for the complete explanation of the influence of cations on the exchange kinetics in the future. Thallium is a transition metal; the size of the Tl(I) ion(r=1.40A) is very close to that of the potassium(I) ion(r=1.33A, r's are the Pauling ionic radii). It provides an opportunity to compare the influence of alkali metal and non-alkali metal cation, on the kinetics of the exchange reactions. The thallium nucleus has the spin of I=1/2, a desirable property for the NMR measurement because of the narrow line-width and good sensitivity of the 205T1 resonance. Because of the similarity of the potassium and thallium ions in their sizes, and because of the good sensitivity of 205T1 NMR, in studies of the influences of charge densities of cations on the exchange reaction kinetics, thallium(I) can also serve as a substitute for potassium, which has a low sensitivity and makes the accurate NMR measurements difficult. 37 Thermodynamic studies are still unable to elucidate unambiguously the nature of the macrocyclic effect. Kinetic studies, generating the reaction rate constants and information of the reaction mechanism, can offer insights into the detailed reaction pathways, and can possibly help to clear the problem of the role of entropy or enthalpy in providing extra stabilities of the cyclic complexes. In addition, there have been very few kinetic studies that deal with the linear polyether ligand complexing metal ions, and any contribution to the kinetic studies of linear ligand complexations would be significant for the further development in this field. In this study, dynamic NMR spectroscopy will be employed to investigate the kinetics of the exchange reactions between the uncomplexed and the complexed metal ions, with a variety of cations(Idf, Na? and Tl‘), 1igands(18C6, 15C5, and pentaglyme), and solvents(THF, DME, AN, and NM) for the objectives given above. 38 Table l. Ionic diameters of cations and diameters of cavities of crown ether molecules(A) Alkali Ionic Crown Cavity metal diameter ether size Li+ 1.35 l4-Crown-4 1.2—1.5 Na+ 1.94 15-Crown-5 1.7-2.2 K‘ 2.66 18-Crown-6 2.6-3.2 Rb+ 2.94 21-Crown-7 3.4-4.3 Cs* 3.34 T1+ 2.80 Reference 8. 39 Table 2. The stability constants of 18C6- and pentaglyme-metal complexes Ligand Cation Solvent Log Kg Reference Pentaglyme Na+ Methanol 1.5 8 18-Crown-6 Na+ Methanol 4.32 8 Pentaglyme K+ Methanol 2.2 8 18-Crown-6 K+ Methanol 6.1 8 Pentaglyme Ag+ Methanol 1.80 77 18-Crown-6 Ag+ Methanol 4.58 77 Pentaglyme Tl+ DMF 0.50 78 18-Crown-6 T1+ DMF 3 . 73 78 40 Table 3. The complexation and decomplexation rate constants of some alkali and alkaline earth cation cryptates in methanol Cations Ligands 0211 0221 0222 .. k, 4.8x105 1.8x107 ---- L1 kd 4.4x10'3 7.5x10 >3x102 .....1},°°.3°..1'>E1.0.6.””unnuiifiioéu ......... 2,721.05.” Na+ kd 2.50 2.35x10‘2 2.87 ;.2.+..].{;...9...0.)£1.0.3..............1...9;(.lbz. ......... 3.512105”. a kd 3.6x10'2 2.3x10'6 2.2x10" w...){f........ ................ 3...8.)(.I0.8” ........ 4271105.... R, 1.09 1.8x10'2 5.2:..ka .......... . ...... ”91.23502...........3...1;‘.16§.... r R, 8.2x10'7 5.5):10'7 Rb+..kf....... ............. o”4...1°x.1.0.8”°””H.71811050.” kd 7.5x10 8.0::10'1 Bazlukfw...” ...... . ...... 11.93503...........5;‘.163...... kd 4 . 6x10'5 6 . 3x10'7 C+kf5x1089x103 S k, 2.3x10‘ 4x10‘ Reference 32,49; k,: M'1 s'1 ; kd: s4. 41 Table 4. Complexation and decomplexation rate constants of lithium and cesium cryptates in various solvents Cryptate Solvent Li(0211)* 05(0222)* kf ko kf kd H20 8.3x103 2.5x10'2 MeOH 4.8x105 4.4x10“ 9x108 4x10‘ EtOH 1.8x10S 6.0x10" MeZSO 1 . 5x10“ 2 . 1x10'2 DMF 1.4x105 1.4x10'2 NMP 1.3x10" 4.8x10'3 PC <3x107 <10'5 5x106 3x102 Reference 58: k,: M‘1 s‘1 ; kd: s”. 42 Table 5. Rate constants of dissociation (kd) , formation (kf) , and formation constants (K,) for the cryptates Ag(C222)+ and K(C222)*in acetonitrile + water mixtures at 25 °C Ag(0222)+ 1((0222)+ x”, '3; """ 12 .267? "@1378” "I; """ REEVES? s'1 M"s'1 M'1 s‘1 M' s‘1 M‘1 0.00 0.4610.01 15.6 34 7.510.8 0.03 0.4 0.05 0.710.l 2.5 3.5 0.1 0.8+0.1 1.3 1.6 3.710.4 0.12 3.2 0.2 1.010.2 1 l 1.1 1.710.2 0.22 13 0.3 1.010.2 1.1 1.1 0.8710.09 0.44 51 0.4 0.6610.07 0.83 126 0.5 1.010.2 1.5 1.5 0.4410.04 1.75 398 0.6 0.3110.03 2.46 794 0.7 l.210.2 2.4 2.0 0.9 0.810.l 4.3 5.4 0.05710.006 11.4 20000 1.0 0.510.l 4.2 8.4 0.004610.0005 11.6 252174 Reference 60. 43 H OCH3COOH {NV/j) mac <10 0 ° 0 (o o] K/OJ CEo 0):: |\/~\/‘ K/KJ Dibcmso- 18- Crown-O Syn- Dibom- 16- Crown- 5 Diue— 18- Crown- 6 D3180. Oxymtic acid DAIOOO £° °J c° Z: 1:: Z: RIF-11%.. O O o ' N O 0 O K/°\/' I l \_/ \___/ 18o Crown-6 13-c -4 C had 1806 T-tmlym 1:51" 3:21 N——(0H,).—N N—-—(CH2).—-T (0H,). 7 (0H,), (CH2) 1 (CH2). N ——(C“2) |-——- N N Massacre“: and linear tetraamine- Volinomycin Nonactin Monactin Dinactin Trinactin Figure 1. Structures of some synthetic and naturally occurring macrocyclic and linear ligands Chapter 2 EXPERIMENTAL SECTION 45 2.1 Purifications of solvents and salts Molecular sieves(3 A or 4 A) were washed with deionized water to eliminate soluble impurities followed by being dried in an oven at 130 °C for a few days and then in another oven at "750 °C for additional few days under nitrogen. These freshly activated molecular sieves were stored in brown bottles in a dry box under helium atmosphere for the future use. Tetrahydrofuran(THF, Mallinckrodt) and 1,2- , dimethoxyethane(DME, J.T.Baker) were refluxed over potassium metal with benzophenone until the color of benzophenone changed to.blue and then fractionally distilled. Nitromethane(NM, Specto purity, EM Science) was dried over calcium hydride under nitrogen atmosphere for 48 hours before distilled. Acetonitril(AN, Specto purity, J.T.Baker) was of spectral grade and contained less than 0.0001% water: it was not further purified except for being stored with the freshly prepared molecular sieves before use. All the purified solvents were stored in brown bottles in a dry box under helium atmosphere. In addition, all the purified solvents were tested by a GC test method described in literaturesnkflv for water contents in order to assure that the solvents contain less than 100 ppm water. All the 46 purified solvents were again treated with the freshly prepared molecular sieves prior to use. Sodium tetraphenylborate(NaBPhb, Gold label, Aldrich) was dried under vacuum at room temperature for 48 hours. Sodium perchlorate(NaClO“ reagent grade, Matheson Coleman Bell) was dried at.1JI)°C for several days. NaSCN(Reagent grade, Mallinckrodt) was recrystalized from acetonitrile and dried under vacuum at 60 °C for two days. LiClO4(Fisher Scientific) was dried at 190 °C for one week. TlClO,,(K&K Chemical Company) was recrystalized from deionized water and then dried at 120 °C for three days. 18-Crown-6(18C6)(Aldrich) was recrystalized twice from acetonitrile and dried in a vacuum oven at room temperature for 48 hours. 12-Crwon-4(12C4, Aldrich) was refluxed at reduced pressure under helium atmosphere and then vacuum dried at room temperature for two days. lS-Crown-5(15C5) was synthesized and purified by a method described by Okoroa for . 8° 2.2 Dynamic NMR spectroscopy 2.2.1 Concepts of dynamic NMR spectroscopy Sparse information available on the kinetics of the complexation of alkali metal ions by macrocyclic crown ethers may be attributed to experimental difficulties in obtaining such data because of the high reaction rates when 47 crown ethers are involved, as well as the lack of color of the complexes which makes spectrometric measurements nearly impossible. The formation of stable ion pairs and of higher aggregates in nonaqueous solvents with low dielectric constants can also lend difficulties to the electrochemical measurements and limit the use of them to high dielectric medium in which there is very little or no ionic association. Dynamic NMR spectroscopy, as compared to the other techniques used for the kinetic measurements, can measure the reaction rates in the middle range.”b In the numerical terms, the dynamic range of this technique is from 10'1 to 10* seconds.73 Generally, the processes of ligand conformational changes, ion pair formations and higher aggregations of ion pairs have faster reaction rates than this limit and cannot be detected by the NMR technique. What are measured by dynamic NMR, however, are the rates of the overall processes (or the rates for the slowest steps) of a series of sequential equilibria. It was discussed previously in Chapter 1 that when metal ions are encountered by neutral macrocyclic or linear polyether ligands, complexation reactions occur. Complexation reactions may be accompanied by conformational changes of the ligands, the dissociation of the ion paris, the desolvations of both the cations and the ligands, and the conformational change of the complexes before the final 48 configuration of the complex is formed. The influence of the ionic aggregations is very important especially in nonaqueous solutions of low dielectric constants. When concentrations of metal ions are greater than that of ligands, exchange reactions for the metal ions between the uncomplexed and the complexed sites exist and proceed by the two mechanisms: the associative-dissociative and the bimolecular mechanisms(Equations 4 and 5, Chapter 1). If one of the steps in the exchange mechanisms has a rate measurable by dynamic NMR, the kinetic information of the exchange reactions can be obtained. This slow step is usually the decomplexation of the exchange reaction while the formation rate reaches the diffusion-controlled range. Thus, by NMR studies, a series of very complicated reactions, which are often times the case in solvents of low dielectric constants, can be "simplified" as an overall one- step exchange reaction, and the important kinetic information such as the reaction rate constants and the activation parameters of the overall reactions can be obtained. An advantage of the dynamic NMR method is that it studies the overall complexation and the exchange reaction kinetics without being interfered by the other side- reactions. The disadvantage is that dynamic NMR is only capable of kinetically studying the chemical reactions at equilibrium--the exchange reactions. Under the circumstance 49 which will be described below, this method is unable to deduce the desired kinetic information from the chemical reaction systems. When the exchange reactions proceed through the associative-dissociative mechanism and the exchange rates are in the dynamic range of NMR spectroscopy(10'1 to 10'6 seconds), the overall rate constants of the decomplexation step kg can be measured and the overall rate constants of the complex formation k, can be calculated through the relation: KF==}q/kd, if the complexation constant K, is known. For the exchange reactions by the bimolecular mechanism, the forward and the backward reactions are identical and so are the rate constants associated with each step. The overall rate constants measured by dynamic NMR are the exchange rate constants and the overall complexation and decomplexation rate constants cannot be obtained. Whether a exchange reaction proceeds by the associative-dissociative or the bimolecular mechanism can be determined by performing dynamic NMR measurement. First, the mean life times of the free and bound metal ions undergoing the exchange reactions at equilibrium are obtained. Through the analysis of the dependence of the mean life times on the metal concentrations, the two exchange mechanisms can be differentiated. Plotting 1/(7[Mmj,) against 1/[M”j, according to the following equation(Equation 6), 50 1 k-2 T[Mm]: [Mm] a straight line should be obtained, either with a zero slope and an intercept of k4, or with a zero intercept and a slope of k4, depending on which one of the two mechanisms predominates. In the above equation, 7 is the mean life time of a metal ion, [Mm]T and [MT] are the total and the uncomplexed concentrations of the metal ion respectively, k, and kQ are the rate constants of the corresponding exchange reaction mechanisms discussed in Chapter 1. If both the slope and intercept are not zero, it is likely that the two exchange mechanisms coexist. Measuring the mean life time 7 of species at different temperatures generates the rate constants as a function of temperature through Equation 6. Arrhenius plots, ln k vs. 1/T(K) or ln (1/7) vs. 1/T, yield activation energies E. of the reactions. From the following Eyring equations, the other activation kinetic parameters can be obtained: 51 111* = 1:a - RT (7) k3 T .AG~ kT = exp( ) (3) RT 110* = 411* - TAS" (9) where k1 is the rate constant at temperature T: AH‘, AG" and As*lare the activation enthalpy, activation free energy, and the activation entropy respectively; kg, h and R are the Boltzman's constant, the Plank's constant, and the gas constant respectively. 2.2.2 Theoretical Aspects of Dynamic NMR Spectroscopy 2.2.2.1 In the absence of the exchange reactions For nuclei not undergoing the exchange reactions between different sites, Block equations in a rotating coordinate at the Larmor frequency v5 along 2 axis have the following forms:81 52 du = (W0 - W) - u/TZ (10) dt dv = -(W° " W) + ierB1 - W/TZ (1].) dt dMZ = -rW°B1 " (M2 " Mo)/T1 (12) dt and W0 = rBo/27r (13) where u and v are the components of the magnetization of the nuclei in the x and y directions in the rotating frame respectively; M5 is the z—component of the magnetization; r is the magnetogyric ratio;1&,is the strength of a static magnetic field in which the nuclei are subject to; B1 is the secondary magnetic field perpendicular to B0 and is used to perturb the magnetization of the nuclei at equilibrium; T1 and.T§ are the spin-lattice and spin-spin relaxation times characterizing the regaining of the equilibria of the magnetizations in xy plane and in z-axis respectively after the magnetizations are perturbed by an impulse of the 53 secondary field B1.'Taking the Fourier transform of the solution of the above differential equations yields: 1 - zni(wo - W) R(W) = 14;. T2 [ (14) 1 + 41r2 T5 (wo - W)J where M; is the magnetization projected on to the y-axis in the rotating frame immediately following the impulse of Br It can be seen that the real part of this equation describes a Lorentzian line in character centered at W0 and the line- width at half-height AW“? can be related to the spin-spin relaxation time Tgiby the following relationship: AW1’2(hZ) = l/WTZ . To describe the relaxations of magnetization of nuclei of metal ions by quadrupolar relaxation mechanism, the relaxation rate (l/Tg) can be related to the spin quantum number I of the nucleus, the asymmetry factor C of the electric field around the nucleus, the quadrupolar moment Q of the nucleus, the 2 component of the electric field gradient d‘aV/dz2 at the nucleus, and the correlation time 7, of the nuclei by the following equation:82 54 1 1 3(21 + 3) (:2 eQ dzv 2 _ = — = (1+—)(—-—;—) Tc (16) T2 T1 4012(21-1) 3 h oz and Er r, = A- EXP[—] (17) RT if I} equals TH under narrowing conditions such as in solutions. To relate the relaxation rate to temperature, by' assuming C2 and d2V/dz2 as constants over the range of temperature, we come to: 1 Er — = A" EXP[—] and (18) T2 RT 1 1 Er 1 1 — = (—) EXPE—(— - _)] (19) T2 T2 298.15 R T 298.15 where (1/T§)8mJ5 is the relaxation rate measured at 298.15 K, T is the absolute temperature and R is the gas constant, 4 Er is the activation energy for solvent reorientation:83 55 Usually, relaxation times Tfitmeasured experimentally are shorter than actual relaxation times T2 due to the magnetic field inhomogeneity caused by the instrumental imperfections such that: = —+—— (20) T2 T2 Tinhomo 2.2.2.2 In the presence of the exchange reactions When nuclei undergo chemical exchange reactions between two nonequivalent sites(without spin-spin coupling), the effect of the exchange reactions on line shapes(or relaxation times) of the two NMR signals corresponding to the two nonequivalent sites depends on the rates of the exchange reactions.“‘Qualitatively, at a very slow exchange reaction rate, two distinct signals are observed, corresponding to the two sites centered at WM and W0,3 with line widths determined by:1/nTu and l/nTn of Lorentzian line shapes respectively, where W, and T2,- are the frequencies and the relaxation times corresponding to site i(i=A or B). In the case of a glow exchange reaction, the similar lines are observed but the line widths 1/«T'uland 1/«T'u are broadened by the exchange reactions, i.e.: 56 and 1/1rT'23 = 1/7rT23 + 1/7r'rB (22) respectively, where TA and 73 are the life times of nuclei at sites A and B. When a exchange reaction is very fast, the two signals coalesce to give a population-averaged signal whose line width 1/Tobs is determined by: 1/Tobs = PA/TZA + PB/TZB (23) where PA and P8 are the relative concentrations of the exchanging species at sites A and B respectively. In the case of a fast exchange reaction, again only one signal is observed but it contains a linebroadening factor due to the exchange reaction: l/T... = 1)./T2. + PB/Tza + Pi PE 2 2 (24") PA PB(|WiA ' Wanna P, and P9 complement each other and can be any numbers in the practical range of 0.1 to 0.9. For Pflfi, it reaches its maximum at 0.25 and its minimum at 0.09. In turn, (P,\P,,)2 is in the range 0.0081 ~ 0.0625 and the average is 0.0353. 58 Substituting this average number into Equation 24", we obtain: 28 (1A + 73) > (24"') (lwo. - Wnl)2 where (IW0A - W08|)2 can be as high as 108(See Chapter 4), thus (rA + 18) > 3 x 10’7 8. indicating that the life times can not be smaller than 10'7 second if the reaction rates are to be measured by the dynamic NMR method. As can be seen from the above equations, in order to derive the life times of 7A and 73, T2, and T23, W, and W3, as well as PA and PB need to be known beforehand. This same requirement also holds for the method of the full-line- shape-analysis to obtain the life times as will be discussed later in this chapter. The NMR lineshape analysis of the kinetic studies of two-site(A and B) exchange reactions can be done by iteratively fitting a theoretical equation, which contains the relaxation times, resonance frequencies of site A and B, and the mean life times of the metal ions, to experimental spectra. This method is called full-line-shape- analysis and is usually assisted by computers. 59 To obtain the theoretical equations of spectra of nuclei undergoing exchange reactions, Block equations describing the motions of xy components of magnetizations of un-coupled sites A and B in the rotating frame as modified to include the effect of the chemical exchange on them 85 are: dMA . .1 4 dt -_d-Mf- = . '1 _ '1 4» (IBM, 1rB1MOB + 7, MA T3 M3 (26) dt where aA = 724 - i(WA — wrf) I as = 72; "' i(wa " er) 7 MA = u, + iWA, Ma=ul3 + 1W8; 7, andra are lifetimes in states A and B respectively;‘WH is the variable frequency; the other symbols have their usual meanings. For pulsed sequence experiments, the signal in time domain is obtained by solving the Block differential equations while B1== 0: 60 d'MA + (a, + 1mm, - 1,1 M3 = o (27) dt (ms + (a, + rg‘ma - r;‘ M, = o (28) dt The solution of the above differential equations is: M(t)=MA+MB=C1er1t+C2er2‘ (29) where C, and C2 are constants and F1 I2 = [-(aA + as + 111‘ + 7&1 t (a, + 7,11 - ozB -- 751)2 + 47);)1 751}1’2]/2. By using the initial conditions immediately after a 1/2 pulse: C1 and C2 can be obtained: C:1 = "iMzo (F2 + 31% + Peaa)/(F1 ' 1"2) c2 = -iM.. (1‘) + Pm + Paaa)/(P1 - r2) 61 To obtain the signal in frequency domain, the Fourier transformation is applied to the free induction decay(FID) in time domain(Equation 29): M(W) = I; M(t)e"<”‘”rf ’ tdt C1 C2 IH ' i(W'WM) I} ' i(W'erf) iMzo [TA + 73 + TATBUIAPB + a8PA)] = (30) [(1 + QATA) (1 + 02873) - l] where 0:A and as have been redefined as following: T5), + i(w, - wrf), 9 > II as = T5; + i(wB - w,,). To accommodate some instrumental corrections, such as an artificial linebroadening and a delay time in order to improve the quality of a signal, and some phase corrections associated with spectra, these equations need to be modified. Strasser/2"“ Ceraso and Dye">8 have discussed at length the influence of chemical exchange reactions on NMR signal line shape in this aspect. The equation(26) has the form after including all the modifications: 62 M(W) = K(Icos[eo -(wA + A - W)DE] — Rsin(80 — (w, + A - W)DE]} + 0 (31) where I = AIMAM(XS) ; R = REAL(XS) c1 Exp[(l"1 - LB)DE] 02 Exp[(I‘2 - LB)DE] X3 = - (32) P1 - LB P2 " LB C1 = 'iMzo (P2 + PAaA + P3a8)/(P1 - I--‘2) C2 = ‘iMzo (F1 + PAO‘A + Paaa)/(r1 "' I‘2) 1"1 1P2 = ["(aA '*' as + 711 + 781 1' {(02A + 7,11 - 0:l3 - 11,1)2 + 47,)1 7&1 )1’2 ]/2. a, = T5} + i(wA - wrf), Q 0 ll 0-3 a)! 63 7A78 7 = __ (33) rA-+ 1, 7A 78 P, - ; PB - (34) 7, + 73 r, + 73 DE and LB are the delay time and line-broadening respectively; AIMAG(XS) and REAL(XS) are the imaginary and real parts of XS respectively. The above equations(31-34) contain information such as the intensity K, baseline C, the zero order phase correction 60, the frequency shift A, and the lifetime 7, the frequencies and relaxation times WA and W3, T2, and T23, of the species in sites A and B respectively without the exchange reaction, the relative concentrations P, and PB of the species in forms A and B. The frequencies(WA and W3) and the relaxation times(Tu and Ta) can obtained by measuring the resonance signals of the nuclei at A and B in the absence of exchange reactions: PA and PB can also be calculated if the equilibrium constant of the reaction is known, or can be directly obtained if the equilibrium constant of is very large. These parameters will be used as known constants in the curve fitting program. The rest of the parameters(K, C, 90,40, and r), referred to as the unknown information, can be obtained by the curve-fitting process. After the lifetime, 7, is obtained, the reaction 64 rate constants can then be obtained in turn because 7 is related to the reaction rate constants as has been discussed earlier in this chapter. 2.3 Procedures of dynamic multi-NMR measurement 2.3.1 Multi-NMR measurement All NMR spectra of UL 7Li, 23Na, and.m”Tl were taken on a Bruker WH-180 spectrometer with Fourier Transform function and equipped with a temperature control unit for variable temperature operations. The spectrometer was operating at a field of 42.27 KG and frequencies of 180, 69.96, 47.61 and 103.88 Mhz respectively for UL,7Li, ”Na, and.“”Tl NMR. Chemical shifts of 23Na, 7L1 and 205T1 in various nonaqueous solutions were referenced to 0.01M NaCl, 1% LiClO, and 0.1M TlClO4:h1IhO respectively, with the corrections for the differences in bulk magnetic susceptibilities of sample solutions and D20 in which the references were contained.86 For Na-23 measurement, the configuration of an insert containing a lock solvent such as D20 or acetone-d6 inside a 10mm NMR tube was implemented for external locking. This geometry was described by Szczygiel.”c The advantage of using this configuration is that the magnetic field of the magnet can be kept from shifting with time and its homogeneity can be conveniently checked and maintained. during measurements. However, the insert itself can cause an appreciable amount of inhomogeneity for signals with 65 extremely narrow linewidths and distort the Lorentzian line shape. In order to avoid such a field inhomogeneity, this configuration was abandoned in the measurements of (Li and szl which have very narrow linewidths--1-4 hz without exchange reactions present. The optimum homogeneity of the field was achieved by shimming the magnetic field carefully every time prior to data acquisition. During the period of data accumulation, the locking circuit was unplugged, and amplitude, level and the sweep width of lock signals were maintained at the minimum level to prevent the field from shifting. 2.3.2 Temperature calibration of the probe for variable temperature studies In order to perform variable temperature kinetic studies, accurate temperatures inside probes need to be known. Usually, temperatures inside probes deviate from temperatures set by a temperature control unit on the spectrometer and deviations are different for each probe. Therefore, a temperature calibration is required for each probe. This was done by measuring the difference of the chemical shifts of the two proton signals of methanol contained in an NMR tube inside a probe at different temperatures. The dependence of the difference of the chemical shifts on temperature was known and measuring the difference of the chemical shifts at a experimentally 66 controlled temperature gives the actual temperature in the probe and the sample tube.87'39 On the WH-180 spectrometer, a Bruker B-ST 100/700 temperature control unit was used to control temperature and a calibrated Doric digital thermocouple was placed 1 cm below the sample tube to measure the temperature. A flow of nitrogen gas maintained the equilibrium of temperature. 2.3.3 Data treatment Since VAX 11/750 system was introduced into chemistry department, the tedium associated with the KINFIT curve- fitting process90 has been greatly reduced as has been the time required for kinetic studies. Strasser72 and the other workers” have thoroughly described the concepts and the steps of computer-aided kinetic studies, and their work is highly recommended for references. Nevertheless, their work had been performed on a different computer system-CDC/750 and, by that time, the punch cards were still used to input data instead of interactively doing so like on VAX-760. Inevitably, the difference of doing the same type of the kinetic studies on the different computers appears to be significant. It is intended in this thesis to ease these differences by stressing how the work is done on the new computer system--VAX 11/750. The following is to show how the kinetic studies by dynamic NMR is done with the help of computers. 67 After a spectrum of the frequency domain is obtained, for the purpose of the line shape analysis, a portion of the spectrum of the interest is chosen by the zoom-function built in the software on the NMR spectrometer. For nuclei in the absence of exchange reactions(either completely complexed or totally free), chemical shifts and relaxation times can be measured by a built-in program called NTCCAP on the WH-180 spectrometer. These information can also be obtained by a method described in Appendix I. The relaxation times and chemical shifts will be used as known constants in the equation of the two-site exchange for the curve-fitting process to get the best fit of the life times 7. In the case when exchange reactions exist, spectra are taken and treated in the same way as are without exchange reactions. After a range of the spectrum of the species undergoing exchange reactions is chosen, this portion of the spectrum is transferred to a file called, for example, TEST.DAT on VAX miniframe computer for the full-line-shape- analysis to derive the lifetime 7. Two programs involved in the data transfer routine, NTCDTL on the Bruker-180 spectrometer and GETNMR(Appendix B) on VAX, are coordinated in a way described in Appendix A so that the data can be transferred from the spectrometer to the VAX miniframe and stored in a data file. An example of this file(TEST.DAT) is shown in Appendix E. At this point, 68 the TEST.DAT file is still not in the correct format for KINFIT program and it needs to be transformed by running NIC180. A copy of this program is shown in Appendix D. The details of the data transformation is presented in Appendix C. After the data transformation, the name of the file is changed automatically to TEST.KIN by NIC180 program. An example of this file is shown in Appendix E. In order to run KINFIT curve-fitting program, additional information needs to be added to the file. A series of the control parameters are at the top of the file, indicating the number of points in the data file to be fitted, the number of iterations to be permitted if convergence is not obtained, the number of constants to be read with each data set and the maximum value of Aparameter/parameter for convergence to be assumed. Aparameter is the change in the parameter from one iteration to the next which should be small to assume convergence. Next line is the title of the file, an identity of the file. Below the title of the file is a roll of constants, given as the known information. The last line before the actual data contains the initial estimates of the parameters to be fitted. A typical example of a file of this kind is shown in Appendix E(TESTK.DAT). The name of the data file for KINFIT program must not be TEST.KIN because the program only reads files with extensions of ".DAT". Thus, the file was named as TESTK.DAT to differentiate it from TEST.DAT and TEST.KIN. 69 Before the data can be fitted to a specific equation by KINFIT, a subroutine that contains the equation needs to be constructed, and to be built into the executable program by running KINBLD.COM(Appendix F). At this point, it is ready to execute the curve-fitting for the data file. The steps of how this is done is given in Appendix H. KINRUN(Appendix G) is a command file that directs how the curve-fitting process to be done on VAX computer. NMRZSITEB(Appendix H) is an executable file that provides the curve-fitting process with the equation that the data in a data are to be fitted. The actual curve-fitting process is carried out by a program called KINFIT. When the fitting is finished, the computer will prompt with the message: Job TEST is completed. If some messages other than this come back, the curve-fitting is failed by some errors. If there is an error associated with the data file, the message will be very indicative and the error can be found and corrected easily. One error frequently encountered is not the error due to the flaw of the data file itself, but the kind intrinsic with the curve fitting process. Simply speaking, in curve fitting processes, initial estimates of the parameters of the interest are provided to the program to start looking for the best unbiased estimate of these parameters. During the "searching" processes, numerous matrices are evaluated by computers. If the initial 7O estimates of the parameters are too distant from the true(or the best unbiased) values, the results of these computations may be over the limit of the capacity of the computers, causing the problem so-called floating overflow. Poor selections of coupled parameters can also cause the floating overflow problem because the values of the matrices are equal to zero and the inverse of zero is indefinite. When the fitting is successful, summaries of the fitting process and statistic analysis are stored in a file with the extension ".REP".(For example, TESTK.REP, which contains the results and the analysis of the KINFIT fitting of the data in data file TESTK.DAT.) Chapter 3 KINETIC STUDIES OF THE COMPLEXATION OF THE SODIUM ION BY 18C6 IN 1,2-DIMETHOXYETHANE AND MIXTURES OF 1,2- DIMETHOXYETHANE AND TETRAHYDRAFURAN 72 3.1 INTRODUCTION As was mentioned in Chapter 1, l,2-dimethoxyethane(l,2- DME) and tetrahydrofuran(THF) have certain remarkably similar properties in terms of density, viscosity, dipole moment, and especially dielectric constant(see Table 6). Both THF and 1,2-DME are etheral solvents, the former having the ring structure with one oxygen donor atom(monodentate) while the latter being a linear molecule with two oxygen donor atoms(bidentate). Usually, metal ions are solvated through ion-dipole interactions, while the donor atoms of the solvents are partially negatively charged. In DME and THF, the sodium ion has a coordination number of four, so that Na(DME)§)and Na(THF)Z can be formed in DME and THF solutions respectively.54 Since the ion pair formations of electrolytes in these two solvents should be approximately the same due to the fact that DME and THF have remarkably similar dielectric constants, the differences in the exchange kinetics should provide information about the differences of the solvents in terms of the solvating powers and their influences on the exchange kinetics. In this chapter, we will present the results of the thermodynamic and kinetic studies on the complexation and the exchange reactions in DME solution, as well as in DME:THF solvent mixtures. Sodium tetraphenylborate and 73 sodium thiocyanate salts and 18C6 ligand were chosen for these studies, because these two salts show totally different kinetic behaviors of the exchange reactions with 18C6 ligand in THF solutions as discussed in Chapter 1; NaClO, was also used to compare the influence of anions on the exchange kinetics. 3.2 Results and Discussion 3.2.1 Solvation and ion pair formation in DME and THF solutions The Gutmann donor number for DME was reported to be 24, a little higher than that of THF(22).72 It has been known that in solvents of low dielectric constants electrolytes tend to form ionic aggregates(pairs, triplets etc.). Both THF and DME have relatively low dielectric constants(7.20 for DME and 7.39 for THF at 25 km, and it has been shown that in these two solvents an appreciable fraction of ions are associated.91 n and Szczygiel73 have measured the equivalent Strasser conductances of NaBPh, and its 18C6 complex in THF solutions. The data are listed in Table 7 together with those obtained in this study for the NaBPh, and its 18C6 complex in DME solutions. Equivalent conductance for the free NaBPh, is about the same in both solvents but it is higher for the Na”18C6 complex in DME than in THF. The above results indicate that the amounts of the ion pairs of 74 the solvated NaBPh, formed in THF and DME solutions are approximately the same, yet the complexed NaBPh, by 18C6 forms appreciably less ion pairs in DME than in THF solutions. The results also show that conductance for the free sodium salt is higher than that of the complexed salt in both solutions. Strasser has attributed this phenomenon to the bigger size and, therefore, the lower mobility of the complexed ions. The possibility of an increased amount of ion pairs formed for the complexed salt should also be taken into account because the complexed ion should has a lower charge density than the free ion and it is easier to form contact ion pairs for ions with lower charge densities. A reason for the about same amount of the ion pair formed for the free salt in both solutions is because the solvating abilities for the uncomplexed sodium ion and the dielectric constants of the two solvents are very similar. More ion pairs for the complexed salt in THF than in DME may be due to the fact that more oxygen donor atoms in a DME molecule(Z) than that in a THF molecule(1) could result in a higher solvation of the complexed sodium ion in DME than in THF. The higher conductance of the complexed sodium salt in DME than in THF could also be due to the size difference of the complexed ion in these two solutions. As mentioned above, DME has a higher oxygen concentration per molecules than THF. More THF than DME molecules are needed to reach a 75 certain stage of the solvation of the complexed ion. Consequently, the solvated Na“18C6 complex is bigger in THF than in DME and the conductance is higher in DME than in THF solutions. 3.2.2 Thermodynamic studies of sodium salt complexes in 1,2-dimethoxyethane Tables 8 and 9 show Na-23 chemical shifts of NaBPh, and NaSCN in 1,2-DME, as functions of the 18C6 mole ratio. The plots of these data are found in Figures 2 and 3. By performing the non-linear least-square curve fitting of these data through KINFIT program,73 the stability constants of the NaBPh, and NaSCN complexes with 18C6 in 1,2-DME solution were obtained: log KF1£:3.95(10.06) for NaBPhgl8C6 and 2.8(1'0.2) for NaSCN°18C6. The stability constant of NaBPh;18C6 complex in THF solution at room temperature is greater than the upper detection limit of the NMR titration method.‘92 In other words, log K, is greater than 4. In DME solutions, Sodium tetraphenylborate forms less stable complex with 18C6 than in THF solution at room temperature. The weaker complex in DME solutions is probably the reflection of a slightly better solvating power of DME than THF, because usually better solvents can more effectively compete for the cations with ligands and consequently reduce the stabilities of complexes. NaBPh, also forms stronger complexes with 18C6 in 76 DME than NaSCN, which is in parallel to the results in THF solutions due to the greater contact ion pair formation of NaSCN than NaBPh,‘ as observed in THF solution. In the case of the contact ion pair formations, anions compete with ligands for cations and weaken the strength of the complexes. 3.2.3 Molecular dynamic studies of the free sodium salts and their complexes by 18C6 In Tables 10 to 14 are listed the chemical shifts and the relaxation times of Na-23 of the free and the complexed sodium salts in DME solution and DME:THF solvent mixtures as functions of temperature. The chemical shifts are plotted in Figures 4 to 8, and the relaxation rates are plotted in Figures 9 to 13 as functions of temperature. For the uncomplexed sodium salts in all solutions and solvent mixtures except for NaSCN in DME, the Na-23 chemical shifts show downfield shifts with the decrease of temperature, while NaSCN in DME practically maintains a constant value for Na-23 chemical shift in the temperature range studied. Generally, both ion pair formations and solvations of the cations increase the electron density around the nuclei of the ions and would contribute to the shielding of the nuclei. At lower temperatures, ions are more solvated and less amounts of ion pairs are formed due to stronger solvating powers and higher dielectric 77 constants(see Table 6) of solvents respectively. The down field shifts of the chemical shifts of the uncomplexed sodium salts with the decrease of temperature reveal that at competition the increase of the shielding effect due to the increase of the solvating power can not compensate for the decrease of the shielding effect due to the decrease of the amount of the ion pairs and the decrease of anions in the immediate vicinity of the cations. As the result, the net electron density around the sodium nucleus is decreased with the decrease of temperature, causing the chemical shifts of the uncomplexed sodium salts shift down field with the decrease of temperature. In the exceptional case of the uncomplexed NaSCN in DME solution, this salt has a very strong tendency to form contact ion pairs (Na‘SCN”), as has been observed in THF solution.72 The increase of the solvating power with the decrease of temperature can easily compensate for the slight loss of the shielding effect from a slight dissociation of the contact ion pairs. Therefore, Na-23 chemical shift of NaSCN is independent of temperature in DME solution. On the other hand, the Na-23 chemical shifts of the complexed sodium salts show upfield shifts with the decrease of temperature with the exception of NaClOy18C6 complex in DME solutions, which shows no change in Na-23 chemical shift with temperature. Usually, for the complexed sodium ion with 18C6, the cation is seated in the center of the cavity of the ligand and is separated or partially separated by the 78 ligand from solvent molecules and anions. The most influential effect on the shielding of the complexed metal nuclei would be certainly from that of the ligands which are in direct contact and interact the most strongly with the complexed nuclei. The interactions between the Na” ion and O-atom of the 18C6 ligand are stronger at lower temperatures, increasing the shielding of the nuclei so that the chemical shifts move to the upperfield(upfield shift). In addition, the higher solvating power of the solvents at lower temperatures would favor the upfield shift too, if the solvent molecules are not completely separated from the complexed cations. For the complexed NaClO, by 18C6, the independence of the Na-23 chemical shift on temperature is probably due to the very weak complexation and the decrease of temperature does not enhance the complexation significantly. The dependence of the relaxation rates of nuclei with quadrupolar moment like sodium on temperature is described by Equations 16 to 19 in Chapter 2. The relaxation rate ln (1/15) can usually be linearly related to 1/T(K) if A' is a constant over the temperature range under an assumption that dZV/dz2 and C do not change with temperature. Both NaClO, and NaSCN in their uncomplexed and complexed forms in DME solutions follow this linear pattern. This behavior was also observed for the uncomplexed and complexed NaBPh, in DME:THF (3:1,molar) mixture, and the uncomplexed NaBPh, in DME:THF (1:1, molar) mixture. For both the uncomplexed and complexed 79 NaBPh, in the pure DME, and the complexed NaBPh, in DME:THF (1:1, molar) mixture, the linear dependence of the relaxation rates on the reciprocal of the absolute temperature does not exist. This observation is probably due to the fact that A' does not remain constant over a range of temperatures, because both d2V/dZZ and C may change with temperature. Another unique feature observed for the NaBPh, salt in 1,2-DME is that the relaxation rate of the uncomplexed salt is greater than that of the complexed salt by 18C6 at temperatures above 266 K, contrary to all the other cases studied in which the relaxation rates of the free salts are always smaller than those of the complexed salts by crown ethers(Table 23). For example, the relaxation rate of the free NaBPhl, in THF is substantially smaller than that of the complexed NaBPh, by 18C6(81 vs. 597 s") . Referring again to Equations 16 to 19 in Chapter 2, the relaxation rate(1/Tg of a nucleus with a quadrupolar moment is inversely proportional to the symmetry of the electric magnetic field around it. Faster relaxation rates correspond to lower symmetries. To summarize, the addition of the 18C6 ligand to NaBPh, decreases the symmetry of the electric magnetic field around sodium ions in THF while it increases the symmetry of sodium ions in 1,2-DME; the free sodium ion has a less symmetric electric magnetic field than that of the complexed sodium ion in 1,2-DME while it the opposite in THF(Table 23). 80 3.2.4 Kinetic studies of the complexations of sodium salts and 18C6 When the concentration of a ligand is smaller than that of a metal ion, at equilibrium, the metal ion undergoes the exchange reaction by one of the two exchange mechanisms as described in Chapter 1(Equations 4 and 5). For NaBPh4-1 18C6, the mean life times for the sodium ions under the exchange reactions were measured by the method described in Chapter 2 at different temperatures in pure DME solutions, and in DME:THF solvent mixtures(1:1, and 3:1). Table 15, Table 16, and Table 17 list the mean life times of NaBPh, with various concentrations of 18C6 ligand in the above solutions respectively. By either exchange mechanisms, plotting 1n (1/7) against 1/T(Temperature) generates slopes proportional to the activation energies of the exchange reactions. These plots are shown in Figures 14 to 16. Since the mean life times of NaSCN and NaClO, are shorter than 10'5 s, stretching the measurement to the limit of the NMR method for the kinetic studies, the exchange rates for the NaSCN + and NaClO,-+ 18C6 systems in DME solutions cannot be measured. Figure 17 shows the plots of 1/7[Na], vs. 1/[Na’], for the system NaBPh, with 18C6 in 1,2-DME at several temperatures. They are characteristic of the associative- dissociative(or uni-molecular exchange reaction mechanism(mechanism II(Equation 5) in Chapter 1). Figures 18 81 and 19 show the same plots in 1,2-DME/THF mixtures. Although there are fewer points in the last two plots, the pattern of the associative-dissociative exchange mechanism can still be readily recognized. The exchange mechanism in the mixtures of DME and THF should be the same as that observed in DME and THF, which is the associative-dissociative mechanism. Tables 18 to 20 show the results of the decomplexation reaction rate constants, kq(or kQ) in consistence with Equation 5 in Chapter 1), of NaBPhgl8C6 complex obtained by the method described in Chapter 2(Equation 6) at several temperatures for the NaBPh4-+ 18C6 system in pure DEM, and in 3:1(molar) and 1:1(molar) mixtures of 1,2-DME and THF respectively. The Arrhenius plots, ln kq‘vs. 1/T(K), for each of the systems listed in the above tables can be found in Figures 20 to 22. 'Table 21 lists the activation energies, Eh, obtained from the Arrhenius plots for the decomplexation reaction of NaBPhgl8C6 complex in pure 1,2-DME, pure THF, and in 1,2- DME and THE mixtures. The other kinetic parameters(see the same table), AH*, AS", AG", were calculated according Equations 7 to 9 in Chapter 2. . The above results have shown quite different kinetic behaviors for the system of NaBPh4-t 18C6 in 1,2-DME from in THF. As can be seen, the difference in the decomplexation rates is more than 2 orders in magnitude: kd== 86001200 s'1 in DME solutions and kd== 5819 s'1 in THF solutions.72 Since 82 the two solvents have almost the same dielectric constants, the ion pair formation of the salt and its complex in 1,2- DME and THF are expected to be about the same and the difference in the exchange reaction rates of the same reaction in these two solvents must reveal some differences in solvation of the sodium ion. Faster decomplexation reaction rates in DME than in THF are also reflected in the weaker stability of the NaBPhg18C6 complex in the former solvent(log K, = 3.95(10.06)) than in THF(log K,>4) . Since K, = kf/kd, where k, and kd are the formation and decomplexation reaction rate constants, and kq‘usually reaches the diffusion-controlled range, it is kg that determines the stabilities of complexes. Activation energies for the decomplexations of the NaBPh518C6 complex are 4.5 i 0.2 kcal.mol'1 in pure 1,2-DME, and 12.2 t 0.5 kcal.mol'1 in pure THF.”'In the binary solvent mixtures, they increase with increasing amount of THF(Table 21) . The other kinetic parameters, AH", AS", AG", show similar trends(either monotonically increase or monotonically decrease with increasing THF)(Table 21). This trend of change of the kinetic parameters with the composition of the solvent mixture is definite and is graphically shown in Figure 23. Assuming the additivity of the kinetic parameters for the decomplexation reaction of the NaBPhgl8C6 complex, we can write: 83 Y = Ymrxmr + YDMEXDME where Y is the value of a kinetic parameter in a binary mixture, Y}'the corresponding parameter in pure solvent 1, and X, the mole fraction of the solvent i in the mixture. The values for each of the kinetic parameters in solvent mixtures can be calculated according to this equation, and compared to those determined experimentally(Table 22). The experimentally determined values do not agree perfectly with the calculated values, but the trend of the change may be roughly predicted by the above equation. Thus, the influence of the solvents on the kinetics of the exchange of sodium ions between the solvated form and the complexed form by 18C6 ligand can be roughly estimated by the relative compositions of the binary mixture. While the kinetic parameters of the exchange reactions are functions of the composition of the binary mixture, the exchange mechanism remains unchanged from THF to 1,2-DME. On the ground of the proposed influence of ion-pair formation of both the free salts and the complexed salts on the exchange mechanism,”’the exchange mechanism would be expected to be the same in DME and THF solutions since the extent of ion-pair formation is approximately the same in these two solvents. That is to say, the associative- dissociative mechanism prevails in both the pure DME and THF solutions as well as in the binary mixtures of these two 84 solvents, simply because the ion pair formations in DME is similar to that in THF solutions. After comparing the NMR study results in pure THF, 1,2- DME and THF:DME mixtures, the question remains why the exchange rates are so much faster in 1,2-DME than in THF, and change gradually with the composition of mixtures in between the two extremes of the composition of solvents whereas the solvating powers and the dielectric constants of the two solvents are very similar. Before answering this question, let us briefly review some of the results about the formation of ion pairs and the dimerization of the ion pairs in DME and THF solutions. Petrucci and co-workers have shown that a competitive reaction mechanism between dimerization of NaBPh, = M to form the dimmers(M2) and its complexation with the 85 macrocycle 18C6 = C to form MC by the following scheme is operative for the NaBPh4-+ 18C6 system in 1,2-DME and THF: k4 M2 -'_ M M k2 k4 M”14 7‘” 2M k1 k3 2M + 2C “‘7 ZMC k5 with overall equation: kf M2 + 20 --* 2MC kd Under this mechanism, different forms of the overall rate constant kg can be derived for two different situations: a) the decomplexation of MC kg is the rate determining step of the reverse process; b) the rate (kg) of formation of the contact dimmer (M2) is the rate determining step of the dissociation of MC.91 The latter explanation, however, suffers a draw back, for that.kg would show a concentration dependence on the ligand, which is demonstrated otherwise by our NMR results. This assumption also requires the overall decomplexation 86 rates to be independent of the type of ligands, which cannot be justified by our results in conjunction with that obtained by Shporer and coworkers.“'It was found that the exchange reaction of NaBPh, between its uncomplexed and complexed site by dibenzo-18-Crown-6(DB18C) in 1,2-DME proceeds by the associative-dissociative mechanism and the decomplexation rate constant of the NaBPhyDB18C6 complex at -12 °0 is 540 s", slower that of the NaBPh,-1806 complex(2800 sq) in DME solutions. The activation energy for the decomplexation reaction of the NaBPh;DBlBC6 complex, 13.3 kcal'mol'1, is also higher than that of NaBPh4'DB18C6 complex, 4.5 1 0.2 kcal.mol”, in 1,2-DME. The other kinetic parameters of the decomplexation reaction, AG‘, AH‘ and AS", calculated from the data given in Shporer's paper, are 11.74 kcal° mol'1 , 12.71 kcal' mol‘1 , and 3.25 cal'mo1’1‘K'1 respectively. The one other major difference in the decomplexation reactions between the systems NaBPhg-+ DBl8C6 and NaBPh4-+ 18C6 in 1,2-DME is that the entropy change is positive when the ligand is DB18C6 while it is negative in the case of 18C6. If the dimerization step of the free salt ion-pairs determined the overall decomplexation reaction, the above results would not be obtained since the overall reaction rate constant under such conditions should be independent of the type of the ligand. Thus, it seems that explanation a) is more reasonable and, that the decomplexation step of the complex determines the overall kg. Usually, the properties of the transition 87 state of a reaction, such as the activation energy and the other activation parameters, are indicative of the easiness of the reaction and reflect the roles of solvents in the reaction. When a multi-step scheme is operative, the apparent activation parameters should closely resemble that of the slowest step. After examining the kinetic results of the overall decomplexations of the NaBPh‘ complex by 18C6 ligand, it can be seen that the activation energy E,, activation enthalpy AHI, and activation entropy AS* are very sensitive to solvents as shown in Table 21. But AH" and AS“ change in the same direction and they offset each other so that the activation free energy AG" is relatively insensitive to the medium(Table 21). The lower activation energy and enthalpy in DME solutions suggest that at the transition state very probably 1,2-DME molecules participate more effectively than THF molecules, lowering the energy level for the transition state of the decomplexation step. The total entropy change from the ground state to the transition state of the decomplexation is composed of two terms: a solvation term describing the involvement of solvents and a ligand term involving the nature of ligands, such as configuration changes of ligands during complexations. The solvation term of the entropy change is determined by two factors: the strength of the solvent-ion interactions(degrees of freedom associated with this interaction) and the number of the solvent molecules involved in the transition state. The 88 stronger the solvent-cation interactions in the transition state, the more strongly the solvent molecules are bonded and more degrees of freedom are lost from the ground state to the transition state of the complex(the more negative AS‘). The more solvent molecules are needed in the transition state, the more negative is the entropy change. DME molecules are more strongly involved in the transition state but fewer of solvent molecules are needed to complete the solvation of the cations in the transition state than for THF. These two factors are opposing each other and the first one(the solvent-cation interactions) must dominate the overall entropy change so that a more negative AS" in DME than in THF results. This favored solvation of the sodium ion at the transition state of the decomplexation by DME molecules probably has the origin of the favored steric effect due to the easier access to the complexed sodium ion at transition state for 1,2-DME molecules because the "concentration" of the oxygen atoms per molecule is higher in DME than in THF. It is well known that the rate of a chemical reaction is determined by the activation energy--the energy difference between the initial and the activated state of the reactant. For the decomplexation of the NaBPhy18C6 complex, the initial complexed form of the sodium ion is at a lower energy level in THF than in DME solutions because of the slightly stronger complexation in THF than in DME. In DME solutions, the energy level of the transition 89 state(activated state) is substantially lower than that in THF solutions due to the better solvating ability of DME at this stage. The net result is that the activation energy for the decomplexation reaction in DME solutions is substantially smaller than in THF solutions. As the composition of 1,2-DME increases, 1,2-DME molecules are available for the solvation of the sodium ion. As a result, the activation energy for the decomplexation is lowered and the decomplexation rate becomes faster. The concept of the involvement of the solvent molecules in transition states of reactions can also be used to explain the faster dimerization reactions of NaBPh, in DME than in THF as determined by Petrucci and coworkers by ultrasonic relaxation method. The results of NaBPhg-+ DB18C6 in DME obtained by Shchori et. alw'also indicate that not only solvents but also ligands play important roles in the decomplexation kinetics. As stated earlier, a total entropy change from a ground state to a transition state of a decomplexation step results from entropy changes of solvents and ligands. DB18C6 is a more rigid ligand than 18C6, and consequently the solvents participation in the transition state of the decomplexation reaction is lessened in the former case: therefore,the entropy change of the solvent in the decomplexation path is less negative. As for the entropy change of DBl8C6 in the decomplexation, it is positive 90 because the ligand is more free and it gains degrees of freedom from the complexed state to the transition state of the complex for the decomplexation. The net effect of these two terms is the slightly positive entropy change for the decomplexation reaction. It is worth noticing that the free energy change of the activation remain almost the same as in the NaBPh4-1 18C6 system. At this point, it is still not clear how slow the rate of the dimerization of the ion-pairs is for NaBPhg in THF. It is possible that this step is so slow that it could couple with the decomplexation rate of the complex and limits the overall decomplexation rate together with the decomplexation step. It is also not clear whether the differences of ion-pair formation of the complexed salts by different ligands would dramatically change the kinetic behavior of the decomplexation, in the cases of NaBPh, with 18C6 and DBlBC6 in 1,2-DME. 3.3 CONCLUSION The complexation reaction of the sodium ion with 18- Crown-6 in DME and THF solutions occurs by a multi-step process, which involves ion-pair formation and ion-pair dimerization. Although it was not investigated in this study, it would be only appropriate to include the ligand conformational change in this scheme since it had been reported by other researchers/'1'21 It was found that 91 dimerization rates are faster in DME solutions than in THF solutions and the decomplexation rates of the overall reaction were shown much faster in DME solutions than in THF solutions, but slower than the dimerization reaction rates in the both solvents. The probability that the dimerization steps in these two solvents are the rate-determining steps is therefore ruled out. Most probably, the decomplexation step of the Na°18C6+ complex limits the overall reaction rates. The difference in the reaction rates in DME and THF solutions suggests that in the transition state DME molecules have a better solvating ability than THF molecules even though the two have similar solvating powers towards the sodium ion in the ground state. 92 Table 6. Physical Properties of 1,2-dimethoxyethane and Tetrahydrofuran as Function of Temperature Temp. Density Viscosity Dielectric °C gram-cm'3 nx103 poises Constant ( 6) THF DME THF DME THF DME 25 0.880 0.859 4.61 4.55 7.39 7.20 10 0.894 0.874 5.42 5.30 7.88 7.60 0 0.904 0.883 6.08 6.10 8.23 8.00 -10 0.914 0.893 6.90 6.70 8.60 8.45 -20 0.924 0.903 7.91 7.80 9.00 8.85 -30 0.934 0.913 9.16 9.30 9.43 9.30 -40 0.945 0.923 10.75 11.30 9.91 9.85 -50 0.955 0.932 12.8 13.8 10.4 10.5 -60 0.966 0.942 15.5 16.9 11.0 11.1 -70 0.978 0.952 19.1 21.0 11.6 11.8 Reference 54. 93 Table 7. The equivalence conductances of NaBPh, Salt and its complex with 18C6 in THF and DME at 28%: Frequency Equivalence conductance, {2'1'eqv"°cm2 in DME in THF (Hz) 0.01M A B NaBPh, NaBPh, NaBPh,’ NaBPhl, NaBPh, NaBPm Complex Complex Complex 398 i 2 19.8 18.0 21.2 16.8 20.98 15.04 629 i 2 20.2 18.5 21.0 16.7 20.86 15.00 971 i 1 20.1 18.4 20.8 16.6 20.75 14.92 1942 i 11 19.9 18.3 20.7 16.4 20.64 14.83 3876 i 18 19.7 18.2 20.5 16.3 20.44 14.68 72 A. Determined by B.Strasser. B. Determined by P.F.Szczygiel.73 94 Table 8. Sodium-23 Chemical Shifts of DME Solutions Containing Sodium Tetraphenylborate" and 18C6 at Various Mole Ratios at Room Temperature Mole Ratio Chemical Shift Mole Ratio Chemical Shift (ppm)‘ (ppm)' 0. -4.47 1 0.1 1.0490 -14.79 i 0.08 0.1299 -5.61 i 0.2 1.0749 -14.89 i 0.08 0.1998 -6.38 i 0.2 1.0989 -14.99 1 0.08 0.2997 -7.40 i 0.2 1.1249 -15.09 i 0.08 0.3996 -8.48 i 0.2 1.1489 -15.15 i 0.08 0.4995 -9.66 1 0.2 1.1748 -15.15 i 0.08 0.5994 -10.58 i 0.2 1.1988 -15.15 i 0.08 0.6993 -11.66 i 0.1 1.2987 -15.20 i 0.08 0.7992 -12.69 i 0.1 1.3986 -15.20 i 0.08 0.8492 -13.40 i 0.1 1.4985 -15.25 i 0.08 0.8991 -13.71 i 0.09 1.5984 -15.25 i 0.08 0.9251 -l3.97 i 0.09 1.6983 -15.20 i 0.08 0.9491 -14.12 1 0.09 1.8981 -15.25 i 0.08 0.9750 -14.33 i 0.09 1.9981 -15.20 i 0.08 0.9990 -14.53 i 0.09 2.1978 -15.25 i 0.08 1.0250 -14.63 i 0.08 2.1978 -15.20 i 0.08 a. Chemical shifts are relative to that of NaCl(0.1M) in D20 at 25.00C0 b. The total concentration of NaBPh, is 0.025M; 95 Table 9. Sodium-23 chemical shifts of DME solutions containing sodium thiocyanate' and 18C6 at Various Mole Ratios at Room Temperature Mole Ratio Chemical Shift(ppm)b 0.0000 '2.5 i 0.2 0.1363 -4.0 i 0.2 0.2982 “4.8 i 0.3 0.5326 ’6.9 i 0.2 0.6007 ‘8.0 i 0.4 0.7925 “9.1 i 0.4 0.8947 -9.5 i 0.3 0.9459 '9.7 i 0.3 1.040 '10.2 i 0.3 1.091 ’10.5 i 0.3 1.376 -11.2 i 0.3 1.542 '11.2 i 0.3 1.901 -11.3 i 0.3 a. NaSCN in 0.0444 M. b. Chemical shifts are relative to that of NaCl(0.1M) in 020 at 25.0°c. 96 Table 10. Sodium-23 relaxation rates and chemical shifts of the free NaBPh‘ and complexed NaBPh‘ by 18C6 in DME solution Temp. Free salta Complexed saltb K T2AX103 (S) 6 (ppm) ° T28X1°3(S) 6 (ppm) ° 298.1 7.2010.07 '4.47i0.09 8.16i0.07 '15.19i0.08 290.2 6.86i0.07 '4.3i0.1 7.83i0.06 '15.20i0.09 282.3 6.39:0.07 -4.1i0.1 7.66i0.05 ‘15.2310.09 274.4 6.35i0.07 '4.0i0.1 7.18i0.04 ‘15.24i0.09 266.5 5.79i0.07 -3.810.1 6.16i0.03 '15.3i0.1 258.6 5.49i0.07 “3.6i0.1 4.17i0.01 “15.4i0.2 250.7 4.25i0.07 '3.2i0.2 2.98i0.01 '15.5i0.2 243.0 3.70i0.07 “2.8i0.2 2.92i0.01 '16.0i0.2 a. 0.0514M NaBPh, in DME solution. b. 0.0519M NaBPhg‘with 0.0600M 18C6 in DME solution. 0. Chemical shifts are relative to that of NaCl(0.1M) in Dzo at 2 5 o 0°C 0 97 Table 11. Relaxation times and chemical shifts ofiBNa of the free NaBPh‘ and complexed NaBPh, by 18C6 in the mixture of DME:THF (3:1, mole fraction) Temp. Free salta Complexed saltb K Tux103 (S) 6 (ppm) ° T2,,xlo3 (S) 6 (ppm) c 298.1 7.91:0.04 -4.8210.08 4.22i0.02 ‘15.5i0.2 290.2 7.8010.04 ’4.76i0.09 3.54i0.01 “15.5i0.2 282.3 7.27i0.03 -4.69i0.09 3.0910.01 '15.6i0.2 274.4 6.46i0.05 -4.7i0.1 2.73i0.02 -15.6i0.2 266.5 6.61i0.03 -4.3i0.1 2.40:0.01 -15.6i0.3 258.6 6.16i0.02 -4.2i0.1 2.00:0.01 ‘15.7i0.3 250.7 5.60i0.02 '3.7i0.1 1.63i0.01 “15.7i0.4 243.0 4.9710.02 '3.7i0.1 1.35i0.01 '15.7i0.5 a. 0. 0522 M NaBPh4. 1.). 0.0481 M NaBPhl, with 0.0651 M 18C6. c. Chemical shifts are relative to that of NaCl(0.1M) in 020 at 25.0°0. 98 Table 12. Relaxation times and chemical shifts ofiBNa of the free NaBPh, and complexed NaBPh, by 18C6 in the mixture of DME:THF (1:1, mole fraction) Temp. Free salta Complexed saltb I< TZAX103(S) 6 (ppm) ° T296103 (S) 6 (ppm) ° 274.4 6.981‘0.04 -6.0i0.1 2.10i0.01 '16.11’0.3 282.3 7.251‘0.05 -6.07i0.09 2.26i0.01 ‘16.0i0.3 290.2 7.60:0.05 ‘6.16i0.09 2.48i0.01 ‘16.01’0.3 298.1 7.911‘0.05 "6.23i‘0.08 2.84i0.01 '15.9i’0.2 306.0 8.54i‘0.07 -6.36i'0.08 3.65i0.01 '15.710.2 313.9 9.3310.07 -6.52i0.07 5.2710.01 '15.5i0.1 13. 0.0484 M NaBPhl, with 0.0607 M 18C6. 0. Chemical shifts are relative to that of NaCl(0.1M) in D20 at 250000. 99 Table 13. Sodium-23 relaxation times and chemical shifts of the free NaClO, and complexed NaClO‘ by 18C6 in DME solution Temp. Free salta Complexed saltb K T296103 (S) 6 (ppm) ° T28X103(S) 6 (ppm) ° 296.5 7.18i’0.07 '7.99i’0.09 4.021’0.02 ’15.4i0.2 285.4 7.26i0.09 ”7.92:0.09 3.891’0.02 '15.5i’0.2 274.4 6.9710.08 ‘7.9i‘0.1 3.87i0.02 -15.510.2 263.3 6.77i0.08 "7.8i0.1 252.3 6.4310.08 -7.7i'0.1 3.571’0.01 '15.5i0.2 241.2 5.52i0.07 '7.3i0.1 3.26:0.01 '15.6i0.2 a. 0.0992M NaClO4. b. 0.1033M NaClO4 with 0.1494M 18C6. 0. Chemical shifts are relative to that of NaCl(0.1M) in 020 at 25.0°0. 100 Table 14. Sodium-23 relaxation times and chemical shifts of the free NaSCN and complexed NaSCN by 18C6 in DME solution Temp. Free salta Complexed saltb K Tux103 (S) 6 (ppm) ° T23x103 (S) 6 (ppm) ° 296.3 4.75i0.05 -2.5i0.1 2.93i0.02 '11.3i0.2 285.9 4.81:0.05 -2.5i0.1 2.82i0.02 -11.4i0.2 276.4 4.73i0.02 '2.6i0.1 2.6510.02 '11.4i0.3 265.3 4.73i0.02 -2.6i0.1 2.49:0.02 '11.5i0.3 255.0 4.58i0.04 -2.5i0.1 2.47i0.01 '11.7i0.3 244.7 4.49:0.03 -2.710.1 2.1210.02 ‘11.7i0.3 a. 0.0400M NaSCN. b. 0.0400M NaSCN with 0.0844M 1806. 0. Chemical shifts are relative to that of NaCl(0.1M) in 020 at 25.0°0. 101 Table 15. The sodium ion mean lifetimes of NaBPh%‘With 18C6 in DME solution Mean life time Temp. 7 (s) x 105 K 1 2 3 4 5 298 10.18i’0.03 6.731’0.13 6.151’0.02 6.03i0.03 3.40i0.04 290 12.2610.04 7.671’0.12 7.45i0.02 6.941‘0.03 3.98i0.04 282 14.081‘0.03 9.98i0.11 7.17i0.04 4.031’0.03 278 11.991‘0.09 8.591’0.03 9.071‘0.04 274 16.15i0.03 12.16i0.09 9.611’0.02 9.77i0.04 3.92i0.03 270 13.43i0.08 10.95i0.04 267 18.88i’0.04 14.201’0.08 13.31i0.02 11.081’0.04 5.65‘1’0.04 259 39.71‘0.2 17.74i0.05 19.711’0.02 11.801’0.04 7.82:0.04 251 49.9i0.1 21.70i0.06 17.521‘0.04 19.8010.06 243 19.89i0.18 19.72i‘0.08 17.62i0.37 235 44.53i0.90 35.30i0.63 1. NaBPh4(0.0507 M) With 18C6(0.0134 M), PM" =0.731; 2. NaBPh4(0.0532 M) With 18C6(0.0280 M), PNa’ =0.4763 3. NaBPh,,(0.0517 M) with 1806(0.0284 M), P"... =0.453; 4. NaBPh4(0.0500 M) With 18C6(0.0302 M), PM" =0.4003 5. NaBPh4(0.0507 M) With 18C6(0.0384 M), PNa‘ =0.249. 102 Table 15(continued) Mean life time Temperature 7 (s) x 105 K 1 2 297.5 6.31 i' 0.03 3.48 i” 0.07 293.0 6.99 i“ 0.02 3.86 i‘ 0.14 289.0 7.63 i‘ 0.02 4.13 i’ 0.11 285.0 8.25 i 0.02 4.94 i’ 0.10 282.0 8.87 i 0.02 4.98 i' 0.09 278.0 9.71 i” 0.03 5.32 i’ 0.12 1. NaBPh4(0.0361 M) With 18C6(0.0168 M), Pug =0.533: 2. NaBPh,,(0.0361 M) with 18C6(0.0212 M), pug. =0.413. 103 Table 15(continued) Temperature Mean life time K r (s) x 105 279.9 13.96 i 0.12 290.7 14.69 i 0.12 294.9 14.82 i 0.11 300.4 13.34 i 0.13 311.0 10.21 i 0.12 318.7 8.62 i 0.15 NaBPh4(0.0375 M) with 18C6(0.0095 M), P“. =0.747. 104 Table 16. The sodium ion mean lifetimes of NaBPh, with 18C6 in the mixture of DME:THF (3:1, mole fraction) Mean life time Temperature 7 (s) x 10‘ K 1 2 298.1 1.35 i 0.01 0.97 i 0.05 290.2 1.96 i 0.01 0.8 i 0.3 282.3 2.73 i 0.02 2.440 1 0.008 274.4 3.80 i 0.03 3.352 t 0.009 266.5 5.92 i 0.07 4.42 i 0.02 258.6 9.3 1 0.1 5.90 1 0.03 250.7 14.6 i 0.3 8.33 i 0.04 243.0 22.2 i 0.6 12.3 i 0.1 1. NaBPh4(0.0491 M) with 1806 (0.0218 M), 13",. =0.556; 2. NaBPh,(0.0520 M) with 1806 (0.0359 M), PM». =0.348. 105 Table 17. The sodium ion mean lifetimes of NaBPh‘ with 1866 in 1:1 (Mole fraction) DME:THF Solution Mean life time Temperature T (s) x 10‘ K 1 2 274.4 6.32 i 0.04 2.00 i 0.01 282.3 5.53 i 0.03 1.94 i' 0.01 290.2 4.48 i 0.02 1.452 1' 0.009 298.1 3.029 i 0.007 0.904 1' 0.006 306.0 1.651 i 0.004 0.470 t 0.006 313.9 1.023 i 0.002 0.482 i 0.007 1. NaBPh4(0.0532M) 2. NaBPh4(0.0514M) with with 18C6 (0 . 0276M), PNu‘ PNa" 18C6(0.0445M), =0.481: =0.134. 106 Table 18. The rate constants of the decomplexation of NaBPhy18C6 complex in 1.2-DME solution Temperature (K) kg (54) 234 1320 i 40 242 1600 i 200 250 2000 i 200 258 2500 i 200 266 3800 i 600 274 4900 i 900 282 5900 i 1000 290 7000 i 1000 298 8000 i 2000 Table 19. The rate constants of the decomplexation of 107 NaBPhleCG complex in DHE:THP(3:1,mole fraction) mixture Temperature (K) kg (54) 243 260 i 15 251 394 i 4 259 600 i 21 267 890 i 70 274 1290 i 150 282 1800 i 300 290 2600 i 500 298 3500 i 800 Table 20. The rate constants of the decomplexation of 108 NaBPhleCG complex in DHE:THP(1:l,mo1e fraction) mixture Temperature (K) kg (54) 314 3400 i 600 306 2500 i 400 298 1800 i 300 290 1200 i 200 282 850 i 80 274 580 i 40 109 Table 21. Kinetic parameters of the decomplexation of NaBPh‘-18C6 complex in THF, 1.2-DME and the mixtures of THF and 1.2-DME at 298 K THF DME:THF DME:THF 1,2-DME (1:1, MF) (3:1, MF) kd 58.19. 18001300 3500:800 8000:2000 E,a 12.2:0.5 7.7io.8 6.8io.2 4.5io.2 AH‘” 11.5:0.5 7.liO.8 6.2io.2 3.7io.2 113*c -11.9i1.6 —20i1 -21.3io.7 -28.2i0.8 A05“ 15.1io.2 13.0:0 12.6io.1 12.1:0.1 a. E“ activation energy, kcal'mol"; b. 1111*, activation enthalpy, kcalmol"; c. AS", activation entropy, ca1°mol"°K"; (1. AG", activation free energy, kcal'mol"; e. kd, (s4). 110 Table 22. The comparison of the experimentally determined kinetic parameters to those calculated THF DME:THF DME:THF 1,2-DME (1:1) (3:1) a.1n Rd 4.1 i 0.2 7.5 i- 0.2 8.2 :t 0.2 9.1 i- 0.3 b. 6.6 7.9 a. E, 12.2 :t 0.5 7.7 i: 0.8 6.8 1' 0.2 4.5 i- 0.2 b. 8.3 6.3 a. 611* 11.5 .t 0.5 7.1 i- 0.8 6.2 i 0.2 3 7 i 0.2 b. 7.6 5.7 a. 60* 15.1 i 0.2 13.0 i 0.1 12.6 i 0.1 12.1 i- 0.1 b. 13.6 12.9 a. 118* -12 i 2 -20 i 1 -21.3 i' 0.7 -28.2 i 0.8 be -2001 -2401 a. Experimental values b. Predicted values c. Ea, activation energy, kcal'mol'13 d. AH", activation enthalpy, kcal'mol’1; e. 118*, activation entropy, cal'mol'1'K'1; f. AG", activation free energy, kcal'mol". 111 Table 23. The comparison of the chemical shifts and the relaxation times of NaBph‘ and NaBPh‘ Complex with 18C6 in THF, 1,2-DHE and the mixture solutions Solvents THF DME:THF DME:THF 1,2-DME (1:1) (3:1) Mole fraction a. Free Salt Chemical -7.55:0.02 -6.01io.08 -4.82:0.08 —4.5:o.1 Shift(ppm) Relaxation 81.1:10% 126.4io.9 126.4io.9 145.610.5 Rate(s.*) b. Complexed Salt Chemical -15.9iO.2 -16.liO.2 -15.5i0.1 -15.19i0.08 Shift(Hz) Relaxation 597.ilO% 351.4iO.9 237.1:0.9 116.2i0.9 Rate(S.”) 112 6, Na-23 chemical shift(ppn) I I r I F I I I I I 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 Cues/Cum Figure 2. Ila-23 chemical shift of NaBPh‘ as a function of the concentration of 18C6 ligand in DME solution at 25°C 113 -2.00 -3.00 a 1 -4.00 - -5.001 1 '1 -6.00~ I -7.00 - -8.00 - -9.00 - I -10.00- -11.00- i 6, Na-23 chemical shift(ppn) ‘I I ‘12-OO'I'r‘Frr'IiI'I'I' “ 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 cuts/Clem Figure 3. Na-23 chemical shift of NaSCN as a function of the concentration of 18C6 ligand in DME solution at 25°C 6, Na-23 chemical shift(ppn) 114 . Free NaPBh‘ “1'00 J ' Complexed NaBPh‘ by 18C6 1 ~3.00 ~ 41.001 -7.00 . -9.00 d 1 -1 1 .00 .. -1 3.00 . 1 -1 5.00 .1 W 1 I -17000 r I I T ' I ' I ' ' I ' I t i 230 240 250 260 270 280 290 300 310 T (K) Figure 4. Na-23 chemical shifts of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of temperature in DME the total NaBPh‘ concentration: 0.05M 115 . Free NaPBh‘ ' Complexed Manph. by 18C6 —1.00- 1 -3.00J ...-5.00 .1 M -7.00 - -9.00- I -11.00- I -13.00- I —15.00d i -17.00J I 6, Na-23 chemical shift(ppm) ”‘gooorlfI'I'r'Ifrfr'I 230 240 250 260 270 280 290 300 310 T (K) Figure 5. Na-23 chemical shifts of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of temperature in DME:THF(3:1,molar) mixture the total NaBPh‘ concentration: 0.05M 116 100 . . Free NaPBh‘ . ,1 . Complexed llaBPh‘ by 18C6 -3.00- E -5.00-( 3 . t M .... -7.00‘ :1 m . '3 “9.00-A 0 .... ‘ 5 g -11.00- 0 n 1 1' -13.00- a z w 6‘ -15.00-( ‘1 W -17.00q -1900 . , - r1 r - . . . _ 1 260 270 280 290 300 31 0 320 T (K) Figure 6. Na-23 chemical shifts of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of temperature in DHB:THF(1: 1,molar) mixture the total NaBPh‘ concentration: 0.05M 117 1 —1,00-4 I -3.00 - .1 -5.00 4 . Free NaClO‘ ' Complexed new, by 18C6 -7.00 - -9.00 4 -11.00-) I -13.00- 1 -15.00-1 I -17.00~ d 6, Na-23 chemical shift(ppm) “'19900'r'I'I'r'Irrfir'rfil 220 230 240 250 260 270 280 290 300 310 '1' (K) Figure 7. Na-23 chemical shifts of the uncomplexed NaClo‘ and the complexed NaClo‘ by 18C6 as functions of temperature in DME the total NaClO‘ concentration: 0.1M 118 0.00- . Free NaSCN ' Complexed NaSCN by 18C6 —2.00« ...—JL———.————-p——IF--I E d 5 -4,oo.. u u -H 1 f1 ... —6.00- a o I .... 8 g -8.00~ ” d 1' £2 -10.00- 8 . -11004 W -14.00 r*r ' r r I " r r I"' r r’I"r I ' I 220 230 240 250 260 270 280 290 300 310 T (K) Figure 8. Na-23 chemical shifts of the uncomplexed NaSCN and the complexed NaSCN by 18C6 as functions of temperature in DME the total NaSCN concentration: 0.04M 119 Free NaPBh‘ I A 5°90. ' Complexed NaBPm by 18C6 ° C o I 0 3 5.701 0 E -H . 4.1 g 5.50- .... u I I N .9. 5.30- 0 H 1 0 5 5.10- g.‘ . ’5, 4.90- B \ I :1 I: 4.70- H 4.50 0.0032'0.0034000365000380.004000542000441 1/T, T: the absolute temperature K Figure 9. The relaxation rates of Na-23 of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of reciprocal temperature in DME the total NaBPh‘ concentration: 0.05M 120 ( . Free NaPBh‘ 7,20. ' Complexed NaBPh‘ by 18C6 ‘? 1 3 3 6.80- 0 . B .... 1" 6.40- c o . .... ‘5 6.00- a H . 3 g 5.604 A u . 5‘,“ 5.20- Q 4.80- 51 c I H 4.40- 4.00 . r ' I f I - r r I ' j 0.0032 0.0034 0.0036 0.0038 0.0040 0.0042 0.0044 l/T, T: the absolute temperature K Figure 10. The relaxation rates of Na-23 of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of reciprocal temperature in DHB:THF(3:1, molar) mixture the total NaBPh, concentration: 0.05M ln (1/Tz), T2: the relaxation time(sec.) 7.20 - 6.80 - 6.40% 6.00 d 5.60 . 5.20 d 4.80 4 4.404 4.00 121 . Free NaPBh‘ I Complexed Nanph, by 18C6 0.0030 0.0032 ' t V I T fi I 0.0034 0.0036 0.0038 l/T, T: the absolute temperature K Figure 11. The relaxation rates of Na-23 of the uncomplexed NaBPh‘ and the complexed NaBPh‘ by 18C6 as functions of reciprocal temperature in DHB:THF(1:1, molar) mixture the total NaBPh‘ concentration: 0.05M 122 6.40- . Free NaClO‘ A ‘ ' Complexed NaClo‘ by 18C6 :3 g 6.00-‘ o a q -H u g 5.60. .M/ .... a o . N .9. a 5.20d . 0 fl . E: 4.80: a d h ~' 4L40- a . H 4.00 0.0032 - 0.0034 ' 0.0036 ' 0.0038 ' 0.0040 ' 0.0042 1/T, T: the absolute temperature K Figure 12. The relaxation rates of Na-23 of the uncomplexed NaClO‘ and the complexed NaClO‘ by 18C6 as functions of reciprocal temperature in mm the total NaClo‘ concentration: 0. 1M 123 6.80 q . Free NaSCN ... ‘ ' Complexed Mason by 18C6 D g 6.40 «4 0 a . 0H J) 5 6.00 - a .... H a: . a: 0 '3 H 5.60 ' 0 A I “ IL—-—1r———1f-'-‘1r__-—.F_—_—A. E: 5.20 - EC“ 1 \ H V 4.80 - : ... ‘040 fi r r I I 0.0032 0.0034 0.0036 r" ' I r “1 0.0038 0.0040 0.0042 l/T, T: the absolute temperature K Figure 13. The relaxation rates of Na-23 of the uncomplexed NaSCN and the complexed NaSCN by 18C6 as functions of reciprocal temperature in DME the total NaSCN concentration: 0.04M 124 6.322506 53 an 603 + «ammo: Imuuhu 0.3 now HRH venison Au); cu .va «Hawk M musuouumlou ousuouns «a» “a .B\H avg-o . 38.0 1 said . 38.0. - 38.086 88.6. . Ovid r snLood . varsd . .nsvh v r I O . I5 0 0 v v v ...-3.. v v . I86. . e . I8: 8.2. ...-n... 383868. 1:83.... :22- 0 . as; ...-... ...-8.868. 1 223.8 4.2... o . Rho ...-.... zen—neon: 1:338 0......n o R... ...-.... 383868— .. x338 4......u a . I86. 086 38.0 ILI . . . «hi6 . 38.0. r 3868.5 88.0. . 86b . grad . grad . 38.184. . f . I86 . f IO... v f v . . I86- 1 v 1 I8..- SNe ...-... ...-3832 1:638 4.23.. o e 2: ..3... ans-.808— : .. 33.8 «...-a- o . Re... .40.... sin-.868. 1.2.3... :2..- 0 an: ...-.... 333.832 1.23.98 e.....nu o r 3'11 8311 "99: an: =4 '(4/1) “I 11.409 .NaBPh‘(0.0491 H) + 18C6(0.0218 H), P.“ = 0.556 INaBPh‘(0.0520 H) + 18C6(0.0359 ll), Pho = 0.348 10.60-* a 1 ...1 v 9.801 ° 1 H 4 ..4 F4 g 9.00“ 3 J I g 8.20- .5.) L. 5 70‘0“ { . H V 6.60- C H 5.80-) 5.00 r . r 0.0031 0.0034 0.0037 1 0.0040 0.0043 l/T, T: the absolute temperature K Figure 15. ln (1/7) against 1/T for the system NaBPh‘-+ 18C6 in DHE:THF(3:1,molar) mixtures 126 ouabph,(0.0532 14) + 18C6(0.0276 II), p... - 0.481 11.004 suabph,(0.0514 I!) + 18C6(0.0134 M), p... =- 0.134 3 3 10.20- 0 u I .... ... : 9.‘O" I 0 a . 0 5 8.60- : d E 7.804 :1 q r: H 7.00- 6.20 r - . 0.0030 7 0.0332 0.0034 0.0036 0.0038 l/T, T: the absolute temperature K. Figure 16. ln (1]!) against l/T for the system NaBPh‘-+ 18C6 in DHB:THF(1:1,molar) mixtures 127 603300 ...—:0 5 003 + .5302 you $.05) .n> :05.) .3 253m 4436 a l-IPD+D savage o sons... 0 accuse e menu... 0 snow... 0 3.03.0 0 l no+uo.u I l no+uo¥ r f 2948.0 8 I 22.8.0 T l 0043. . 11.911] 4/t 128 083x2— .uouolJfiimaumxo 5 003 4 3.302 new .705} .u> £03.} .3 0.33m Josue-u O ppm-¥ Java... 0 .705} a snow... 0 [OOQL D D D b P D a 1. some... 0 1886 0 Dog D TD D D D 1. D D sauna I .82.. o r. 3.484 I ¢o+ucd I r. no+uué l 00.73.. 8 :3... a r. no+uo.« ‘[.9H]£/I 129 1/1 ["301 4.5E-l-05fi '1 . at 270 k e I at 282 k 4.0E+05- .‘ at 290 k ‘ 0 at 298 k 3.5E+05- V at 306 k y 0 at 314 k 3.0E+05- 2.551054 ZOE-+05- 1.5E+05- O 1.0E-l-05- - O 5.0E+04- 0.0 7 “ 'FTI'I'I'ITI'I‘ 0 20 40 60 80100120140 1/[Na’lr Figure 19. ]./1'[Na]t vs. 1/[Na’], for NaBPh‘ + 18C6 in DHE:THF(1:1,molar) mixture 130 lnkd 1 I 7-00 r f I I r T ' I 1 I ' r ‘ 0.0031 0.0033 0.0033 0.0037 0.0039 0.0041 0.0043 1/1', '1': (K) Figure 20. The Arrhenius plot for the system of NaBPh‘ + 18C6 in the pure DME solution. In L; vs. 1/T 131 9.00 - 8.20 - 7.404 lnkd 6.60 - 5.80 - 5.00 -. , - ...1, .- ,_ 0.0031 0.0034 0.0037 0.0040 0.0043 l/T, T: K Figure 21. The Arrhenius plot for the system of RaBPh‘ + 18C6 in DHB:THF(3:1, molar) mixture. ln 1L; vs. 1/T 132 9.00 - 8.20 - 7.404 ln kd 6.60 «4 5.80 d 5.00 -...... 0.0030 0.0032 0.0034 ' f 0.0036 0.0038 l/T, T: K Figure 22. The Arrhenius plot for the system of NaBPh‘-+ 18C6 in DHE:THF(1:1, molar) mixture. in IL; vs. l/T 133 o.— mmaumxa mo ousuxwl hussfin on» no :oHuwmoaloo 058 Mo usowuossu no unauoasuom newus>wuod .nm chumam mg 0:0 H29 #6 «.0 8 D D D b -- 33333333 No nonsuxwl when“: an HIE Ho awash 0H0! .Uix 33333333 on. so one so «no one on. cue one one ed 1 - - 1 - as 11 1 1 ed w 8* 3 a. a I ... 4 Go. .nl .... .... . ed. 1 ed. mm 63 A. at 31 m1 «3 as 1 - so 1 - 1) 11 - ed. 661 V 0.01 a... W 3....” .... 3.1 a m. . .. .:l1.w a 931». ...... 6.81 .. "an! Chapter 4 KINETIC STUDIES OF THE EXCHANGE REACTION OF THE THALLIUH ION WITH 18C6 AND PENTAGLYHE IN ACETONITRILE 135 4.1 INTRODUCTION As noted before, kinetic studies of complexation reactions of metal ions with macrocyclic ligands are sparse as compared to thermodynamic studies. Open chain ligands or linear ligands have even less kinetic information available, probably because most of the exchange reaction rates of metal ions between their uncomplexed sites and complexed sites are too fast to be measured by most of currently available experimental method. Maass and coworkers,‘93 describe the synthesis of a series of noncyclic neutral ionophores and studies of the complexation reactions of these ligands with alkali metal ions by . The formation rate constants are in the range of 107 to 1081r‘s”, which are relatively high but still lower than the value of around 109 to 101° Dr‘s" expected for a diffusion-controlled combination of alkali metal ions with complexones in methanol solutions. The reduced rates are a consequence of the stepwise replacement of the solvent molecules in the inner coordination sphere of the metal ion by the chelating atoms of the multidentated complexone. This study is one of the few that deal with the linear ligand kinetic study with metal ions. As has been discussed in Chapter 1, the tremendously enhanced macrocyclic complex stabilities(the macrocyclic effect) compared to that of their linear ligand counterparts 136 are still inconclusive as to which of the two factors, enthalpy or entropy, is predominant.”39 Kinetic studies can provide information of complexation(kq) and decomplexation(ka) rates as well as on the exchange mechanism. If the stability constant K“¢,of a complex is known, measurement of k, and kd can show which of the two factors, the complexation or the decomplexation, determines the stability of a complex since Ksm, = k11/kd.38 Hopefully, kinetic studies of complexation reactions of ions with linear polyether ligands can yield useful kinetic information about these linear ligands and possibly help to elucidate the nature of the macrocyclic effect. 4.2 RESULTS AND DISCUSSION 4.2.1 Molecular dynamics of the uncomplexed thallium ions and the complexed thallium ions by lB-Crown-G and pentaglyme To perform the kinetic study of the exchange reaction kinetics, the chemical shifts and the relaxation times of both the uncomplexed and the complexed thallium salts have to be measured as functions of temperature. The results of these measurement are listed in Tables 26 to 28. The chemical shifts of all species, the uncomplexed and the complexed thallium ions by 18C6 and by pentaglyme, show very clear dependence on temperature(See Figure 24); the resonances shift up-field with decrease of temperature. The 137 up-field shifts of the resonances indicate a stronger solvent-cation interactions for the uncomplexed and ligand- cation and/or solvent-cation interactions for the complexed cations at lower temperatures(See Page 76). However, the relaxation times of the free thallium ion and the complexed thallium ion by 18C6 do not follow the linear relationship with the reciprocal of temperature as described by Equation 19 of Chapter 2(See Figure 25). This observation is probably due to the fact that the linewidths of the free and the complexed thallium signals are extremely narrow and any inhomogeneity of a magnetic field can cause large errors in the measurement of an extremely narrow linewidth. The inhomogeneity can be caused by the geometry configuration of the experimental arrangement of NMR tubes(lock solvent in the insert) or by the field shifting because no insert with lock solvent used to avoid the inhomogeneity caused by an insert as discussed in Chapter 2. 4.2.2 Kinetic studies of the exchange reactions of TlClO‘ with 18C6 and pentaglyme in acetonitrile solution When the concentrations of the ligands are smaller than the total concentrations of the salt, thallium ion undergoes the exchange reaction between the uncomplexed and complexed forms. The mean life times of the thallium ion were measured at several temperatures. The results of this measurement at different concentrations of the thallium ion and of the 138 ligands are listed in Table 29 for the 18C6 and in Table 30 for the pentaglyme respectively. The results show that the mean life times of the thallium ion are approximately one order in magnitude longer with 18C6 than with pentaglyme, indicating a faster exchange reaction in the TlClo‘ + pentaglyme system than in the TlC104-+ 18C6 system in acetonitrile. In order to obtain the mechanisms of the exchange reactions in these two systems, 1/[Tlfhr is plotted against 1/[Tij. In Figures 28 and Figure 29 are shown these plots for the TlClO4-+ 18C6 and TlClo‘-+ pentaglyme systems in acetonitrile, respectively. Horizontal straight lines are obtained in the case of TlClO4-+ 18C6 at all temperatures the measurements were made, indicating that the bimolecular mechanism prevails according to Equation 6 of Chapter 2. It is evident that in the case of TlClO4-+jpentaglyme system the exchange reaction is a combination of the bimolecular and associative-dissociative mechanisms. With the decrease of temperature, the contribution of the associative- dissociative mechanism is gradually reduced. At 263 K, the exchange proceeds only by the bimolecular mechanism. For pentaglyme, the plots of 1/[TIUTT vs. 1/[Tlfih also separate the respective contribution of the two exchange reaction mechanisms to the overall reaction rates, yielding k, and k-2(or kd) corresponding to the bimolecular and the associative-dissociative exchange mechanisms respectively. 139 The above results show that the exchange mechanisms of TlClO‘ between its uncomplexed and complexed sites in acetonitrile solutions are different for the different ligands. The rate constants for the respective reactions for the TlClo‘ + 18C6 and TlClO‘ + pentaglyme systems are listed in Tables 31 and 32 respectively. The Arrhenius plot (ln kh‘VS. l/T) of the TlClO‘-+ 18C6 system in acetonitrile is not linear(See Figure 30). Figure 26 show the plots of In (l/r) vs l/T for the system TlClO4-k 18C6 in acetonitrile solutions at different relative ratios of TlClO,, to 18C6. These plots also show a generally decreasing slope with decreasing temperature. Figure 27 shows the plots of ln (1/1) vs 1/T for the TlClO‘-+jpentaglyme system. The exchange reaction in this system is a combination of the associative-dissociative and bimolecular exchange mechanisms, and ln (1/1) vs l/T plots give the activation energy of the exchange reaction only when one of the exchange mechanisms is dominant. Figures 31 and 32 show the Arrhenius plots of the two exchange mechanisms for the system TlClO‘ + pentaglyme in acetonitrile solution. The activation energies E, of reactions can be obtained from the Arrhenius plots, and then the other activation 140 kinetic parameters (AH*, AG‘, and AS*) can be calculated. According to the equation: Ea ln k = A - RT where k is a reaction rate constant, R and T the gas constant and temperature(k), 1n k is linearly dependent on l/T with intercepts of A and slopes of 22,/Rm. the activation energy of the reaction). The nonlinearity of Arrhenius plots can be caused by the change of either A or E; or both with temperature. However, it could not be justified to conclude which, A and E" cause the nonlinear behavior of the Arrhenius plots for the TlClo,-+ 18C6 and TlClo‘ + pentaglyme systems in acetonitrile solutions. If assuming that the A is a constant over the temperature range studied, the change of the slope of the plots of ln k against l/T can be attributed to the variation of E. with temperature. The purpose.of this assumption is to roughly asses the solvent influence on E. and exchange mechanisms at different temperatures, and it should not be taken literally. For the system of TlClo‘-+ 18C6, the activation energy decreases with the decrease of temperature. It is ”16 kcal'mol‘1 at 328k, ”2 kcal'mol’1 at 298k, and “0.3 kcal-mol'1 at 278 respectively. For TlClO‘-+jpentaglyme, plots of In Hg) and In (kq) vs l/T give activation energies of 141 3.00:0.05 kcal'mol'1 for the bimolecular exchange mechanism, and temperature dependent activation energy for the associative-dissociative mechanism(‘S kcal'mol'1 at 298k and ”'11 kcal'mol'1 at 263k) . The other kinetic parameters of the exchange reactions are listed in Table 33. Since only the exchange reaction rate constants can be determined by NMR measurement if the exchange reactions proceed by the bimolecular mechanism, the complexation and decomplexation reaction rate constants are not obtainable. It is not possible to compare the complexation and decomplexation rate constants to see which of the two dominates the stability constants. However, the enhanced stability(>1oo times) of the macrocyclic complex Tl'18C6*(log Kf=5.810.5)8° over that of the linear complex Tl'PG*(log Kf=3.65i0.05)5° is probably a combination of the complexation and decomplexation steps. The Tl'PG“ complex is less stable than the Tl'l8C6’ complex and the decomplexation rate is faster for the former. The formation rate constant at 298 k for the Tl'PG+ complex is 9.8 x 103 s", as obtained in this study by using the relationship Kf=kf/kd where K, and kd are known. According to Maass,"3 the formation rate constant of the Tl'PG” complex is slower than the diffusion-controlled rate constants(lo9 to 1010 s”). The slower formation rate constants of linear ligands than expected for the diffusion-controlled processes are a result of the step-wise substitution of the solvent 142 molecules in the solvation shells of cations. The more rigid pre-arrangement of the donor atoms of the macrocyclic ligands before complexation cations can more effectively replace the solvent molecules in the solvation shells of cations. It would be reasonable to expect that the complexation of the thallium ion by 18C6 is faster than the complexation by pentaglyme and may reach the diffusion- controlled limit. The faster complexation rate of the thallium ion and the slower decomplexation rate of the complexed thallium ion in the Tl*-+ 18C6 system than Tl*-+ pentaglyme system combine to give a loo-fold more stable complex for the former. Apparently, there is an interdependence between the nature of ligands and the resulting exchange mechanisms since different mechanisms prevail for different ligands in our study. It has been discussed before, that ion-pair formations and solvating abilities of solvents greatly influence the exchange reaction rates and mechanisms. In general, based on the electrostatic repulsions of like charges and the entropy terms, the associative- dissociative mechanism is favored over the bimolecular mechanism. This preference can be changed if the charge- charge repulsion can be substantially reduced by formation of contact-ion pairs, or strong solvent—cation interactions, and so forth. The energy barrier of the decomplexation(EJ is also determined by the easiness of the release of the 143 ligand. If a ligand strongly interacts with a cation, the decomplexation will be difficult, especially in solvents of very poor solvating abilities, and the activation energy E2 will be high. In order to explain the different behaviors of TlClO‘ with 18C6 and pentaglyme in acetonitrile solutions, solvations, contact ion-pair formations, and the roles of ligands, will have to be considered. In 0.01 M thallium perchlorate acetonitrile solutions, the ion pair formation of the salt should not be significant. The solvent does not have very high solvating power, as evidenced by the low solubility of TlClO‘ in this solvent(”0.01 M) . It seems that neither the ion pair formation nor the salvation of thallium ions by the solvent is able to reduce the cation-cation repulsion at the transition state of the exchange reaction intrinsic with the bimolecular mechanism. Let us assume that the exchange reaction proceed through the associative-dissociative mechanism for a system in which ion pair formation is limited and where the solvent has a very weak solvating power. At the transition state, the ions have to be partially decomplexed, but probably not solvated by the solvent molecules due to the poor solvating power of the solvent, resulting in high energy level of transition state. For the same system, the energy level of the transition state of the bimolecular mechanism would be even higher, considering the cation-cation repulsion at this 144 stage. Logically, the exchange will have to follow the associative-dissociative pathway so as to avoid the higher energy requirement by the bimolecular mechanism. If ligands can interact with cations sufficiently strongly so that the cation-cation repulsion is reduced, it is possible that the bimolecular mechanism can still exist. In acetonitrile, both the TlClOgl8C6 complex and the TlClOyPG complex are stable but the former is about 100 times more stable than the latter. Therefore, the bimolecular mechanism becomes possible for both the Tl*-+ 18C6 and Tl*-+jpentaglyme systems. For the Tl*-+ 18C6 system, the cation-ligand interactions are so strong that the bimolecular mechanism is the only exchange pathway throughout the studied temperature range. The situation for the TlClOg-+ PG system in acetonitrile solutions is a little different--the two exchange mechanisms coexist at room temperature and the bimolecular exchange mechanism dominates at low temperatures. In this system, the ligand-cation interaction is not as strong as that of’Tflf-IBCG, and this interaction cannot effectively offset the cation-cation repulsion at the transition state of the bimolecular mechanism. This weaker complexation of'Tflf-pentaglyme is responsible for the competition of the associative- dissociative mechanism with the bimolecular one. At low temperatures, the increase of the cation-ligand interaction can assist to decrease the cation-cation repulsion at the transition state and the bimolecular mechanism prevails. 145 It should be mentioned that configurations of ligands may also play an important role in determining the exchange mechanism. 18C6 is a cyclic ligand, and has a symmetrical plane for cations to approach from the both sides which makes the bimolecular mechanism likely to occur. Pentaglyme is a linear ligand and it has a more free configuration than 18C6, enhancing difficulties for the symmetrical and simultaneous bonding of cations to the ligand occurring in the transition state of the bimolecular mechanism. At lower temperatures, the structure of the ligand is more rigid and more likely to take crown-ether like configurations, leading to the more contribution of the bimolecular mechanism to the overall exchange process. Another important factor that should be mentioned for the observed bimolecular mechanism in our study is the charge density of the Tl+ cation. It is known that K’ and Tl“ have very similar sizes and therefore the similar charge densities(see Table 24). It is also known that for K’ ion the exchange mechanism is often bimolecular. Table 25 lists some results of the kinetic studies of the complexation reactions of thallium and potassium with crown ethers. Schmidt and coworkersfi’have found the bimolecular exchange mechanism for the potassium ion between its uncomplexed form and the complexed form by 18C6 in acetone, 1,3-dioxolane, methanol solutions, and in the mixture of acetone-1,4- dioxolane(80:20 v/v). The exchange mechanism in water“ was found to be the associative-dissociative one. In pure 146 acetone, methanol solutions and the mixture of acetone-1,4- dioxolane, the exchange rates were found to be in the range of lo5 M'1s" to 10" M"s" in pure 1,3-dioxolane solutions. The decomplexation rate in aqueous solutions was determined to be 105 to 106 s". For Tl'l8C6” complex, the exchange proceeds through the bimolecular exchange mechanism and the activation energy for the decomplexation reaction decreases with decreasing of temperature in the temperature range of 278 - 328 K. The decrease of E, with temperature can not be explained by the increased ion-ion interactions which reduce the cation- cation repulsion at the transition state of the bimolecular exchange mechanism, and eventually reduce the activation energy, because the dielectric constant of the solvent increases with decreasing of temperature and the ion-pair formation decreases with the decrease of temperature. The only other cause that can reduce the activation energy for the decomplexation reaction is the stronger solvating power of the solvent at lower temperatures although acetonitrile has been considered as a weak solvating power solvent. It is reasonable to imagine that the solvating powers of solvents increase with decreasing of temperature because motions of cations, solvent molecules and other particles are slowed down by decreasing temperature, and solvent molecules have longer time to interact with cations. Consequently, the change of the activation energy for the 147 exchange reaction with temperature could be the direct result of the better solvating power of acetonitrile solvent at the lower temperature range. Based on the obtained resutls, a detailed exchange scheme may proposed as following: Tl*'L + 'T1* + ns 2 Tl’mL + 'T1* + ns (1) Tl""L + 'T1’ + ns 2 T1‘ + L + *T1* + ns (iia) or Tl""L + *T1* + ns 2 Tl""'L"" *Tl’ + ns (iib) T1""'L"”‘T1’ + ns :2 3N2 ..... Tl“'"L""‘T1* ..... 3N2 (iiia) s,,,2 ----- T1*----L~--"r1" ----- sm 2 T1’ + *Ti-L +ns (iiib) or T1*----L----"r1* + ns 2 T1’ «1 *n-L + ns (iiic) where s is solvent and the other symbols have their usual meanings. For a poor solvent, it is unlikely that the solvent will participate in this scheme. For a weak complex, steps iiia will not occur because the complex decomplexes before the second metal ion ('Tl‘) reaches it. Thus, for the Tl”PG complex, the exchange reaction undergoes by steps i and iia resulting in an associative dissociative mechanism. On the other hand, the Tl“18C6 complex is stronger and a bimolecular mechanism prevails for the exchange reaction. That is, at high temperatures when the solvating ability of acetonitrile is weak, the mechanism is consisted of steps i, . iib, and iiic while at low temperatures when the solvating power is high the mechanism is composed of steps i, iib, iiia, and iiib. 148 4.3 CONCLUSIONS By comparing the activation energies and their temperature-dependence for the exchange reactions of Tl+ ions with 18C6 and pentaglyme, it is clear that the strengths of the cation-ligand interactions and the structures of the ligand are important factors in determining the exchange mechanism. At the kinetic points of view, the bimolecular exchange reaction mechanism is not favored by the entropy factor, but the enthalpy factor is so strongly favored that it can overcome the entropy influence and the bimolecular exchange mechanism prevails for the system of TlClo‘-+ 18C6 in acetonitrile solutions and for the system of TlClO, + pentaglyme at low temperatures. Because of the bimolecular exchange mechanism in the system TlClO4-+ 18C6, the decomplexation rate constant of the complex cannot be obtained. Thus, we are not able to compare the two systems to conclude which factor, complexation or decomplexation, determines the macrocyclic effect. 149 Table 24. A list of some physicochemical properties of some metal ions Alkali Crystal Charge Free energy Rate constant metal radius density of hydration of inner sphere substitution r[A] [Coulomb/A3] k[s4] Li 0.60 0.22 122 ‘5 x 108 Na 0.95 0.088 98 “8 x 10' K 1.33 0.045 81 ~1 x 109 Rb 1.48 0.036 76 ~2 x 109 Cs 1.69 0.029 68 '5 x 109 T1 1.40 Pauling ionic radii 150 Table 25. Comparison of the complexations of thallium and potassium M Solv. KF k1 1 kd Ref. 0830c10 K+ neon (3.7:0.4)x10" (6:2)x108 (l.6i0.5)x10" 21 quf neon (3.2:0.4)x10‘ (8:1)x108 (2.5:0.3)x10‘ 21 18C6 K+ 1&0 1.0x101o 3.7x106 20 K‘ MeOH 1 . 26x106 95 K+ cascu 5x105 25 , 97 15cs K+ 150 5.5:0.5 4.3x108 7.8x107 24 T1+ 150 17:2 8.0x108 5.0x107 24 151 Table 26. Tl-205 chemical shift and relaxation time of the free thallium perchlorate(0.01M) in acetonitrile Temperature Chemical Shifts Relaxation Time (K) (PP!!!) (S) 333 -209.0410.02 0.0180i0.0008 328 -211.1110.02 0.0l72¢0.0007 323 -213.1510.02 0.0154i0.0004 318 -215.21i0.02 0.0177i0.0004 313 -217.34i0.02 0.0171i0.0006 308 -219.84i0.02 0.0187i0.0002 303 -221.6510.01 0.023110.0002 298 -223.45¢0.02 0.0204i0.0002 293 -225.30i0.02 0.0170i0.0003 288 -227.87i0.03 0.0089i0.0001 278 -232.3510.03 0.0090:0.0001 268 -237.2810.02 0.0143i0.0002 258 -242.3110.02 0.0138i0.0001 248 -247.20i0.02 0.0124i0.0002 t — The chemical shift is referenced to that of 0.1M TlClO4zh1 D20 0 152 Table 27. T1-205 chemical shift and relaxation time of the complexed thallium perchlorate(0.01M) by 18C6 in acetonitrile Temperature Chemical Shifts Relaxation Time (K) (PP!!!) (S) 333 -142.75i0.03 0.0101i0.0002 328 -143.83i0.03 0.0119i0.0003 323 -144.89i0.02 0.0141i0.0004 318 -146.02i0.02 0.0181i0.0004 313 -147.84i0.01 0.0232:0.0005 The chemical shift is referenced to that of 0.1M TlClO‘:h1 020 . 153 Table 28. Tl-205 chemical shift and relaxation time of the complexed thallium perchlorate(0.01M) by pentaglyme in acetonitrile Temperature Chemical Shifts Relaxation Time (K) (PP!!!) (S) 298 ~139.5810.02 0.0150i0.0008 288 -142.20i0.03 0.0080i0.0004 278 -l44.98£0.09 0.003510.0001 268 -148.3tO.2 0.00189i0.00007 258 -152.47iO.2 0.00123i0.00007 248 -156.59i0.3 0.00088i0.00003 The chemical shift is referenced to that of 0.1M TlClO‘:h1 020 e 154 Table 29. The mean life times of the thallium ion in the system of TlClO‘ with 18C6 in acetonitrile solutions Mean life time Temperature 1 (s) x 10‘ K 1 2 3 4 278 2.57:0.02 2.44:0.03 3.28:0.07 2.4710.06 288 2.19:0.03 2.2610.02 2.69i0.03 2.19:0.02 293 2.21:0.02 2.14:0.05 2.92:0.09 2.34:0.05 298 2.30:0.03 2.2810.02 2.5810.06 2.5310.01 303 2.17:0.02 2.17t0.01 2.48:0.03 2.2310.03 308 1.9510.01 1.88:0.02 2.48i0.05 2.16:0.02 313 1.6610.01 1.7010.02 1.91:0.04 1.73:0.02 318 1.51:0.02 1.45:0.01 1.762t0.03 1.26:0.02 323 1.25:0.03 0.93:0.05 1.5910.07 1.32:0.04 328 1.23:0.04 1.3910.08 1.4110.07 1.7610.07 1. T1C104(0.0112M) with 18C6(0.0045M), Pn+ = 0.5946; 2. T1C104(0.0100M) with 18C6(0.0015M), PM“ = 0.8487: 3. T1010,(0.0099M) with 18C6(0.0094M), P". = 0.0894; 4. T1C104(0.0097M) with 18C6(0.0074M), PIP = 0.2394. 155 Table 30. The mean life times of the thallium ion in the system of TlClO‘ with pentaglyme in acetonitrile Mean life time Temperature 1 (s) x 107 K 1 2 3 4 308 2.55:0.05 2.74:0.06 2.5310.05 2.17:0.05 298 3.8010.05 2.8710.05 1.9410.04 293 3.04:0.07 3.6410.05 2.81:0.05 2.2210.09 288 3.53:0.06 3.19:0.03 3.77:0.03 4.2710.06 283 5.1:0.2 3.8i0.1 3.2i0.1 3.0:0.2 278 5.1:0.l 4.0iO.1 3.4iO.1 5.3:0.2 273 3.3:0.2 4.910.2 4.6:0.2 3.2iO.3 263 8.5io.5 7.0iO.3 6.4i0.3 6.2:0.5 l. TlClO4(O.OlO7M) with pentaglyme(0.0034M), Pn+ = 0.6822: 2. TlClO4(O.OO95M) with pentaglyme(0.004lM), Pn+ = 0.5653; 3. T1c1o,,(0.0099M) with pentaglyme(0.0056M), p". = 0.4311; 3. TlClO,,(0.0097M) with pentaglyme(0.008lM), Pn’ = 0.1678. 156 Table 31. The exchange rate constants(k1) of the thallium ion in the system of TlClo‘ with pentaglyme in acetonitrile via the bimolecular exchange mechanism and the exchange or the decomplexation rate constant(kd or k-2) via the associative-dissociative mechanism, T1c1o, : 0 . 01M Temperature 19 x 10'8 kQ x 106 (k) 1(1'34 s4 308 3.5 i 0.1 3.1 i 0.4 298 3.0 i 0.1 2.2 i 0.4 293 2.7 i 0.1 1.9 i 0.4 288 2.5 i 0.2 1.6 i 0.4 283 2.3 i 0.3 1.3 i 0.5 278 2.1 i 0.2 1.0 i 0.5 273 1.9 i 0.2 0.8 i 0.5 253 1.5 i 0.2 0.4 i 0.6 157 Table 32. The exchange rate constants of the thallium ion in the system of TlClO‘ with 18C6 in acetonitrile , TIClO‘ : 0 . 01M Temperature k, x 10'7 (k) Dr‘s“ 278 3.7 i 0.5 288 4.2 i 0.4 293 4.1 i 0.5 298 4.1 i 0.2 303 4.4 i 0.3 308 4.7 i 0.4 313 5.5 i 0.3 318 7. i 1. 323 8. i 2. 323 6.8 i 0.6 158 Table 33. The kinetic information of the exchange reactions of TlClO‘ in acetonitrile solutions with 18C6 and pentaglyme at 298k k E, - 611* AS‘ AG.~ l8-Crown-6 (4.1iO.2)xlO7 ~2 ~1.4 “-19 7.06:0.03 Pentaglyme A (3.0:0.1)x108 3.00:0.05 2.4110.05 -11.6¢0.2 5.88:0.02 B (2.2:0.4)x10s '5 “4.4 ‘-19 10.2:0.1 a. 8,, AH", and AG", in units of kcal'mol": AS“ in the units of cal'mole‘1 'K"; b. k: the decomplexation rate constant.kg corresponding to the associative-dissociative mechanism in acetonitrile solutions with the units of s”: or the exchange reaction rate constant k, of the bimolecular exchange mechanism in nitromethane solutions with the units of S“LM”: c. AN is an abbreviation for acetonitrile and nitromethane respectively: d. The bimolecular exchange mechanism: 18-Crown-6 and pentaglyme(A): the associative-dissociative mechanism: pentaglyme(B). 6, Tl-205 chemical shift(ppm) Figure 159 __120_: 0 Free TlClo‘ in All I Complexed TlClO‘ by 18C6 in AN 1 ‘ Complexed T1Clo‘ by PC in All -140- 1 l"' —160- .1 —1804 —200-4 -220~ —240~ -260 .1 ... .1. r4. ,1.+r,.+1., 240 260 280 300 320 340 T (K) 24. Tl-205 chemical shifts of the uncomplexed TlClO‘ and the complexed TlClO‘ by 18C6 and pentaglyme ligands in acetonitrile solutions as functions of temperature O 6 1 "08.0 $8.0 008.0 —§.O R” 0.0 rlLllrlLllhlIPILllhllrllland.IIPILIIPILIIPIlrlLllrllTenn. 24523 «CACHE poxuanfloo 0 ounuauumfiou Ho m:0fiuo:§u mm mcowusdom uawuuflflouwoa :« munuwwd oflhammucmn can 603 an .083 60.83500 05 6:6 .082. cuxmamflooss 058 no wanna :owumxcuou mONIHB .mN unamwm M ousunuoalou ousaouAG «an "a .B\H I H086 068.0 38.0 38.9 hung. at 5 603 as «OHUHB vuflodnloo o 0:36 9236 onad p983 bfiaa D I 5 5 .083. 000m . “via '80 In.“ IoQa land I 38 (mama-n Immune: an: :31. '(21/1) at the mean life time T: ln (1/1), I 1330- 1350- “JO-i IZJO- 1230 161 0 P". = 0.5945 4 o P". = 0.850 d 13.00- 13.50- 43.10-- 12.70- 1230 ......‘...1.1'..1..'...:1..'..1.1 '“.....'..1.1'1.1..'..1..113..1 C D . P74. 3 0.101 . Pft'. a 0.237 I q '..1..‘..:1.;..1..'..1.1 ”......1111'1113'1111233 A ' B 1/T, T: the absolute temperature K Figure 26. ln (l/r) vs. 1/T for the system TlClo‘ + 18C6 in acetonitrile solution 1: the mean life time(s) of the thallium ions in the exchange reaction: T: temperature in K: A. 0.009914 now, + 0.008%! 18C6, p“. = 0.101: B. 0.009714 T1010, + 0.007414 18C6, p". = 0.237; 0. 0.011214 TlClO‘ + 0.004514 18C6, p". = 0.5946: 0. 0.010014 T1010, + 0.001514 18C6, p". = 0.850. 162 “.21 II Pno = 0.5653 J a Prt’ 3 0.6822 " d iSJJ . 4 .1 18.0-4 . .1 I d . I J ‘” 14.4-4 1 l .3 I, J u a ' a 133-J a ...q H '1 d g ‘3': U r U ‘l: I V T g a 1 06&u1 onkn' 03L“! 00G“ Oflkflb oaknr OJLMI o C D .E .u a 10.24 9 P": = 0.1678 4 I Ptl‘ :3 0.4311 Q 1 q E 13.0-J . :1 d .1 ‘3 15.0"‘ d - H I 4 1 - 144 4 d I . J 13.3-1 .1 d d ‘12 1 . . 13.2 , , , i Ohkflb OJLN' 00L“! 00G“ Oflkfll Oflkfl' 03L“! A B l/T, T: the absolute temperature K Figure 27. In (1/1) vs. l/T for the system TlClo,-+ pentaglyme in acetonitrile solution. 7: the mean life time(s) of the thallium ions in the exchange reaction: T: temperature in K: A. 0.009714 T1010, + 0.008114 90, p“. = 0.1678: B. 0.009914 T1010, + 0.0056M pa, 9... = 0.4311: 0. 0.009514 T1010, + 0.004114 pa, 9". = 0.5653: 0. 0.010714 T1010, + 0.003414 pc, 9". = 0.6822. 163 Figure 28. 1/r[Tl*]I vs. l/[Tl’]F for the system TlClO, + 18C6 in acetonitrile solution at several temperatures 7: the mean life time of the thallium ions in the exchange reaction(s): [TI‘]t and [Tlfh: the concentrations of the total and free thallium ions respectively 164 89.8. 8. _- — .L . 11.1.41... 71!...» .381... ...-«In __ ...... gibbibb I r u m1 H W/mm. :9...- ..an :31 o r ...-u.- a 0 g nnnn ad bbbbbb 1- j I! O I I OJ U I 150.98.. F 3+8... 165 Sam>fluowmwwu wcofl Esfiaamnp mwuu 0:0 Hmuou on» no mCOMHMHHQTOCOO Tau “IFHBH 0:0 CFHBH “amvso«uomwh mmcmnoxo 0:» ca mcofl Edwaaazu 0:» mo was» mafia some on» “s mmusumuwmlmu HOH0>um um GOMuzaou wafluuwcoufloa a“ wflhamwusom + .033. 830.0... 05 you .731} .m> £93.} .3. 0.30: 173;) 33808:. [Ir-lrLl-ll06 [lLILI-llg [ILllrlrllod [Ilrpl—ILILI I V I use. 0 I V f I I I I I I I I I I .31.. .310. gain. .81.. .510 ‘8'.- I 0.0 I 8+8; I 8.78.8 I 8.98.0 I 80.8.9 I 8.98.0 I 8+8.- 1 0.0 I 00.98.— I 00.98.“ I 00.78.». I 00.78% I 00.78.“ 1[JIM/I ln 1:, 19.001 1 10.00- 1 10.00- 1 18.40d 1 18.204 18.00-‘ J 17.80- I 17.00-1 I 17.40- J 17.20 - I 166 b 1 7.00 0.0030 I I I l I r r r 1 I r I I l 0.0031 0.0032 0.0033 0.0034 0.0035 0.0030 0.0037 1/T, T: K Figure 30. 1n 1:, vs. l/T for the system TlClO, + 18C6 in acetonitrile solution. lg: the exchange rate constant of the thallium ions by the bimolecular mechanism: T: temperature in K 167 20.10- 10.”- 10.30- ln k, 10.20- 10.00- 10.0-4 10.30 r Figure 31. 1n 1:, vs. l/T for the bimolecular exchange mechanism in the system TlClO, + pentaglyme in acetonitrile solution )9: the exchange reaction rate constant of the thallium ions by the bimolecular exchange mechanism: T: temperature in K 168 13.” -I 12.20- 11.40- ln L; l 1°.”- 0.” - 1/1'. T: K Figure 32. 1n k41vs. l/T for the associative- dissociative mechanism in the system TlClO,-+ pentaglyme in acetonitrile solution k¢: the exchange or the decomplexation rate constant of TlClO(Pentaglyme complex by the associative-dissociative exchange mechanism; T: temperature in K Chapter 5 KINETIC STUDIES OF LITHIUH PERCHLORATE COMPLEX BY 15- CROWN-S IN ACETONITRILE AND NITROHETHANE 170 5.1 INTRODUCTION Kinetics of the exchange reaction between the free lithium salts and their complexes by macrocyclic polyethers have been studied much less than those of the other alkali ions. The lack of kinetic information for Id? again can be attributed to the experimental difficulties encountered in the measurement. The acquisition of kinetic information by the NMR technique involves measurements of the relaxation times of the free and of the complexed metal ions, as well as obtaining the spectra of the nuclei of the metal ions under exchange conditions. It is very difficult to accurately obtain the information mentioned above when the line widths of the measured signals are very narrow. Without exchange, lithium line-widths are typically between 1 to 2 Hz and they are 5 to 8 Hz with exchange. In addition to the measuring difficulties, the fact that the lithium ion forms only a few stable crown ether complexes , e.g. with 12C4, and 15C5, and in only a few solvents, such as acetonitrile and nitromethane, limits the kinetic studies to a small number of systems with high enough complex stabilities and slow enough decomplexation rates for dynamic NMR measurement. Previous studies on sodium, potassium, and cesium ions have helped to understand the mechanisms of exchange 171 kinetics. The exchange reactions basically occur through two different mechanisms, bimolecular and unimolecular(or associative-dissociative) mechanisms. The lack of the kinetic information about the lithium ion makes it difficult to draw any conclusions about how cations would influence the exchange reactions. It is our goal to study the exchange kinetics of lithium salts in order to see the influence of the cations on the exchange reactions. 5.2 RESULTS AND DISCUSIONS 5.2.1 Molecular dynamics of the uncomplexed lithium perchlorate and the complexed lithium perchlorate by 15C5 in acetonitrile and nitromethane solutions Tables 34 to 35 contain relaxation times and chemical shifts for the Li’-+ 15C5 system in acetonitrile and nitromethane solutions respectively. These data are plotted as functions of temperature in Figures 33 to 34. All species show that the chemical shifts move upfield with decreasing temperature, indicating stronger solvations for the uncomplexed lithium ions and stronger ligand-cation interactions for the complexed lithium ions respectively at lower temperatures. For the free salt in both solutions, the relaxation rates (ln (1/T§)) follow the dependence on temperature predicted by Equation 19 of Chapter 2, that is, increasing with decreasing of temperature. For the complexed form in the solutions, the relaxation times are more or less 172 randomly distributed with temperature. This temperature randomness of the relaxation times for both the free and the complexed sites by cryptands was also observed in other solvents, such as pyridine, dimethyl sulfoxide, and dimethylformamide, formamide, and water.“’The cause for this observation may result from a good number of factors, such as solvations of the cations, ligand-cation interactions, the viscosities of the solutions and so forth, which all change with temperature in a variety of ways. 5.2.2 The kinetics of the exchange reactions of lithium salts in acetonitrile and nitromethane solutions Tables 36 to 37 list the mean life times of lithium perchlorate undergoing exchange reactions between its free and complexed sites, at various free and the complexed concentrations of the salt in acetonitrile and nitromethane solutions respectively. The plots of 1/1[Li"]T vs. 1/[Lifh show the very strong characteristics of the unimolecular or dissociative-associative exchange mechanism in acetonitrile solutions(Figure 35), while in nitromethane solutions the bimolecular exchange mechanism is followed(Figure 36). The exchange reactions undergo different mechanisms in different solvents, namely, the associative-dissociative mechanism(Equation 4, Chapter 1) in AN and bimolecular mechanism(Equation 5, Chapter 1) in NM. From the plots of 1/7[Li"]1 against 1/[Lifir shown in Figures 35 and 36, the rate constants for the respective exchange reactions are 173 obtained according to Equation 6 of Chapter 2--namely, the intercepts and the slopes of these plots are obtained as the rate constants for the bimolecular and the associative- dissociative mechanisms respectively. These rate constants are listed in Tables 38 to 39. Figures 37 to 38 show the plots of the natural logarithm of the reciprocal of the mean life times(ln (1/1)) against the reciprocal of the absolute temperature(l/T). The activation energy for the decomplexation of the LiClO{15C5 complex in acetonitrile and the activation energy for the exchange reactions in nitromethane are 4.8310.03 kcalmmflf‘ in acetonitrile solutions and 4.98:0.09 kcal'mol'1 in nitromethane solutions respectively. The activation energies can also be obtained by plotting 1n k vs. l/T (Arrhenius plots)(see Figures 39 and 40), where k is the rate constant and T is the temperature(K). When only one exchange mechanism is operative for exchange reactions, plots of ln (1/1) vs. l/T differ from plots of In k vs. l/T only by a constant while the slopes are the same. The activation energies are listed in Table 40 together with the other kinetic parameters: 11H", AS“, and AG”. The study of the exchange kinetics of the lithium complexes by 12-Crown-4 has also been attempted, but the reaction rate was so fast that it was not possible to measure the mean life times of the complex in the temperature range studied. 174 As can be seen, lithium ion complexation by 15C5 in acetonitrile and nitromethane is very fast(the mean life times are in the range of 107 to 10* seconds)(see Tables 36 and 37). The activation energies are small, compared to those of the lithium-cryptand complexes,“’which are usually in the range of 10 to 20 kcal°mol". As usual, the smaller activation energies for the decomplexation is a result of weaker lithium-crown ether complexes than the lithium- cryptand complexes. Naturally, 3-dimensional cryptand macrocyclic ligands have better complexing abilities toward metal ions(the "cryptand effect") The decomplexation of the cryptand complexes is more difficult compared to the 2- dimensional crown ether complexes in which the complexed cations are still exposed to the solvent molecules. Among crown ethers, lithium salts form the strongest complexes with 15C5 ligand because the cation size is closest to that of the 15C5 ligand cavity(see Table 1). The logarithm of the stability constant log K, for the lithium perchlorate complex with 15C5 in nitromethane and acetonitrile solutions is greater than 4."8 Generally, other lithium-crown ether complexes are less stable and the decomplexation rates are very fast--to a degree that the mean life time of the lithium species can not be measured. Summarizing the kinetic results of the exchange reactions involving the alkali ions and some crown ethers in acetonitrile and nitromethane solutions, we can see two 175 interesting patterns of the exchange mechanisms for the alkali ions in these two solvents. The exchange of the lithium ions between its uncomplexed site and the complexed site by 15C5 in acetonitrile and nitromethane solutions proceeds by the two different mechanisms: the associative-dissociative and the bimolecular one respectively. In a study of Detellier and coworker,“ the exchange mechanism of the sodium ion with DB18C6 and DB24C8 in acetonitrile was shown to be the associative-dissociative one and in nitromethane the associative-dissociative and the bimolecular exchange routes are competing with each other.“ For the potassium ion complexed by crown ethers, no exchange kinetic information is available in acetonitrile and nitromethane solutions. But the thallium ion resembles the potassium ion in the charge density, and can be used as a substitute for the potassium ion for the purpose of comparing the influences of cations of the alkali family in kinetic studies as discussed in Chapter 1 and Chapter 4. According to the results presented in Chapter 4, the thallium ion undergoes exchange in acetonitrile solutions between the uncomplexed and the complexed sites through the bimolecular exchange mechanism when the ligand is 18C6, and the combination of the associative-dissociative and the bimolecular mechanisms while the ligand is pentaglyme. 176 Shamsipur“ has reported on the kinetics of the exchange reactions of Cs+ with DB30C10 in acetonitrile and nitromethane solutions. The associative-dissociative mechanism is a predominant one in nitromethane solutions whilst the bimolecular exchange path way is a prevailing process in acetonitrile medium. Clearly, the results mentioned above show that in acetonitrile solutions the exchange mechanism changes from the associative-dissociative one for the lithium ion to the bimolecular one for the cesium ion. The change of the exchange mechanism in nitromethane solutions follows the opposite direction, namely, the bimolecular mechanism for the lithium ion and the associative-dissociative mechanism for the cesium ion. In order to understand the different patterns of the exchange mechanisms for the alkali ions in acetonitrile and nitromethane solutions, we first invoke the discussions about the roles of the ion pair formation and the solvating powers of the solvents. Solvents of good solvating powers as well as contact ion pairs can effectively reduce the cation-cation repulsion encountered in the transition state of the bimolecular exchange reactions as noted by Shamsipur“ and Strasser,so because the presence of solvents and anions in the immediate vicinity of cations can partially offset the charge densities of the cations. Usually, contact ion pairs tend to 177 form more easily in solvents of poor solvating abilities because ionic species can be solvated by solvents of strong solvating abilities to prevent the formation of contact ion pairs. The Gutmann donor number for acetonitrile is 14.7, substantially higher than that of nitromethane(2.7), while the dielectric constants of acetonitrile(38) and nitromethane(36) are comparable. The combined effect of a slightly lower dielectric constant and a much smaller solvating strength of nitromethane than acetonitrile is that electrolytes tend to form more contact ion pairs in nitromethane solutions and cations are more solvated in acetonitrile solutions. As discussed previously, the associative-dissociative mechanism is favored over the bimolecular mechanism on the grounds of entropy and cation-cation repulsions. Which one of the two exchange mechanisms dominates in acetonitrile and nitromethane varies from cation to cation and depends on the strength of solvations of cations and ligands, and the amount of the contact ion pair. Naturally, it is more difficult to form contact ion pairs for the lithium ion than for the other alkali ions since it is strongly solvated due to its high charge density. Contact ion pairs are increasingly formed as one goes from lithium to cesium, and the exchange mechanism leans more and more to the bimolecular process. This is exactly what was observed in acetonitrile solutions: the 178 ’ associative-dissociative mechanism for the lithium sodium ions and the bimolecular mechanisms for the potassium(resembled by In?) and cesium ions. Since it was reported that in acetonitrile lithium perchlorate forms a contact ion pair,”’it is logical to expect that lithium perchlorate also forms contact ion pairs in nitromethane solutions. Consequently, for the lithium ion an appreciable amount of the contact ion pairs formed in nitromethane solutions would help to diminish the cation- cation repulsion so that the bimolecular exchange mechanism can prevail. However, the pattern of the change of the exchange mechanisms for the alkali metal ions between their uncomplexed sites and their complexed sites by the crown ethers in nitromethane solutions contradicts the above assertion of the influence of contact ion pairs on the exchange mechanisms. If purely following the argument of contact ion pairs to explain the exchange mechanism, we will be unable to conclude why the exchange mechanism in nitromethane solutions is the associative-dissociative one in the Cs‘-+ DB30C10 system and the bimolecular one for the Li+ + 15C5 system since Cs“ should form more contact ion pair than.1df due to the lower charge density of the former. Thus, the influence of other factors need to be considered for the exchange mechanisms. § 179 Shamsipur“’assumed that for the cesium ion the solvent with stronger solvating power(acetonitrile) helps reduce the cation-cation repulsion in the transition state of the bimolecular exchange mechanism and in the solvent of a poor solvating ability(nitromethane) the associative-dissociative mechanism is preferred. This argument cannot be extended to the lithium ion in acetonitrile solutions because Id? is more strongly solvated than the cesium ion and should undergo the exchange reactions by the bimolecular exchange mechanism, which is in contrary to the obtained results. Neither the formation of contact ion pairs nor the solvation of the cations can be used alone to explain the patterns of the change of the exchange mechanisms of the ions throughout the family of the alkali metals in acetonitrile and nitromethane solutions. Usually, when interpreting the exchange kinetics, the roles of ligands are ignored. However, Boss100 has reported that some crown ethers and linear ligands react with some solvent molecules to form adducts. The results of the complexation are tabulated in Table 41. From these results, some trends among the studied ligands can be roughly recognized: a) the larger ligand are more solvated: b) the crown ethers are more solvated than the linear ones: c) the ligands are more solvated in nitromethane than in acetonitrile: d) the benzene- substituted crown ether is more solvated than the un- substituted counter part in acetonitrile and it is the opposite in nitromethane. Without doubt, the complexation of 180 ligands with solvents(or solvations of ligands) will have influences on the exchange kinetics. Solvations of ligands stabilize the partially decomplexed ligands at the transition state of the associative-dissociative mechanism, contributing to the existence of this mechanism or the competition of this mechanism with the bimolecular one. Exchange kinetics and exchange mechanisms are complicated by ion pair formations, and by solvation of both cations and ligands. To explain the observed results, only preliminary speculations can be made. Further investigations are badly needed to achieve a better understanding. The lithium ion is highly solvated in acetonitrile solutions due to its high charge density, and contact ion pairs are formed in nitromethane due to the low dielectric constant and the low solvating ability of the solvent. As the result, the associative-dissociative mechanism prevails in acetonitrile solutions while the bimolecular mechanism is favored in nitromethane solutions. The sodium ion still prefers the associative-dissociative mechanism in acetonitrile solutions because of the solvation of D818C6 and DB24C8 and because the charge density of the sodium ion is still high: in nitromethane solutions the two exchange mechanisms coexist because of the more contact ion pairs formed due to the lower dielectric constant and the less benzene-substituted ligand-solvent interactions. The results for the thallium ion were shown above and in Chapter 4, namely, the bimolecular exchange for the ligand 18C6 and the mixture of 181 the two mechanisms for the ligand pentaglyme because of the preferred ligand geometry of 18C6 for the bimolecular mechanism and the decreased charge density of the thallium ion. For the cesium ion, the more contact ion pairs formed and the bigger and more symmetric DB30C10 ligand prefers the bimolecular mechanism in acetonitrile solutions while the weaker solvation of the cesium ion in nitromethane solution leads to the associative-dissociative mechanism. 5.3 CONCLUSION It is clear that the exchange reactions for the lithium ions in these two solvents undergo totally two different mechanisms. Doubtless, both charge densities of cations and properties of the solvents have significant influences on the exchange reaction kinetics as evidenced by the patterns of the exchange reactions associated with each alkali cation in acetonitrile and nitromethane solutions. From lithium to sodium, potassium and then to cesium ions, the exchange mechanism goes in acetonitrile solutions from the associative-dissociative to the bimolecular exchange mechanism, while in nitromethane solutions it is a bimolecular one the lithium ion and a associative- dissociative one for the cesium ion. These patterns are tentatively explained by the currently available knowledge of the influences of the ion pairs of electrolytes and the solvations of the ligands and cations. 182 Table 34. Lithium-7 relaxation times and chemical shifts of the free LiClO, and complexed LiClO, by 15C5 in acetonitrile solutions Free salta Complexed saltb Temp . T2, 6 ° Temp . T2B 6° (K) (8) (ppm) (K) (S) (ppm) 297 0.122:0.007 -2.359¢0.004 300 0.10710.005 -1.758£0.004 285 0.107i0.006 -2.502i0.004 290 0.114i0.006 -1.915i0.004 275 0.092:0.005 -2.616i0.005 280 0.103:0.007 -2.044i0.004 265 0.081i0.003 -2.731i0.006 270 0.099i0.006 -2.187i0.005 255 0.07010.003 -2.845i0.007 260 0.113:0.004 -2.345i0.004 250 0.100i0.006 -2.502£0.005 a. 0.0991M LiClO, in the acetonitrile solution; b. 0.101014 LiClO, with 0.152811 1505 in the acetonitrile solution: 0. Chemical shifts are referenced to that of LiCl(1%) in 020 at 25 °C. 183 Table 35. Lithium-7 relaxation times and chemical shifts of the free LiClO, and complexed LiClO, by 15C5 in nitromethane solutions Temp. Free salt‘ Complexed saltb K T211 (S) 6(ppm)° T2. (8) 6(ppm)° 298 0.12010.005 'O.640£0.004 0.10810.002 '1.48810.004 290 0.10710.006 '0.71510.004 0.10710.007 -l.587io.004 282 0.10110.005 -O.79810.005 0.10910.007 -1.660i0.004 274 0.10310.005 '0.87610.004 0.12210.007 '1.750i0.004 266 0.09910.005 -O.964io.005 0.072i0.003 '1.841$0.006 258 0.09510.006 '1.05210.006 0.10610.003 '1.917io.001 a. 0.0498M LiClO, in the nitromethane solution: b. 0.0500M LiClO, with 0.0683M 15C5 in the nitromethane solution: 0. Chemical shifts are referenced to that of LiCl(l%) in 020 at 25 °0. 184 Table 36. The lithium ion mean life times of LiClO, with 15C5 in acetonitrile solutions at different relative concentrations of the salt to the ligand Mean life time Temperature 1 (s) x 10‘ K 1 2 3 300 2.010.1 5.5:0.2 ----- 290 1.810.1 5.810.4 ----- 280 2.610.2 8.610.3 2.lio.2 270 4.210.2 19.010.6 2.510.2 260 7.310.3 22.9iO.6 3.910.3 250 1011 2912 5.4io.4 1. Li01o,(0.102014) with 15C5(0.0506M) in the acetonitrile Solution, PU+== 0.504: 2. LiClO,(O.1039M) with 15C5(0.0350M) in the acetonitrile Solution, P”. = 0.663: 3. LiClO,(0.1020M) with 15C5(0.0720M) in the acetonitrile Solution, PW = 0.294. 185 Table 37. The lithium ion mean life times of LiClO, with 15C5 in nitromethane solutions at different relative concentrations of the salt to the ligand Mean life time Temperature 1 (s) x 10‘ K 1 2 3 4 298 1.0:0.1 2.2:0.2 2.7io.3 0.810.2 290 1.210.1 3.2i0.2 3.2io.2 1.1i0.3 282 1.4:0.1 3.7:0.3 3.810.2 1.3:0.2 274 1.7:0.2 4.3i0.2 4.6iO.3 1.8:0.2 266 1.9:0.2 4.9io.2 5.8:0.3 2.410.2 258 3.010.1 74.:0.2 10.1i0.4 3.110.2 1. LiClO,(0.0521M) with 15C5(0.0216M) in the nitromethane solution, P”. = 0.586: 2. LiClO,(0.0465M) with 15C5(0.0366M) in the nitromethane solution, PU+== 0.215: 3. LiClO,(0.0334M) with 15C5(0.0277M) in the nitromethane solution, PU+== 0.170: 4. LiClO,(0.0766M) with 15C5(0.0175M) in the nitromethane solution, PU+ = 0.772. 186 Table 38. The decomplexation rate constants of LiClo, complex by 15C5 in acetonitrile solutions at different temperatures Temperature kd x 10'3 (k) 300 2.5 i 0.4 290 1.9 i 0.3 280 1.4 i 0.2 270 1.0 i 0.1 260 0.7 i 0.1 250 0.49 H- O O 00 187 Table 39. The exchange reaction rate constants of LiClO, complex by 15C5 in nitromethane solutions at different temperatures Temperature )9 x 10* (K) 298 15 i 4 290 12 i 3 282 9 i 2 274 7 i 1 266 5.3 i 0.9 258 4.0 i 0.6 188 Table 40. The kinetic information of the exchange reactions of LiClO, in acetonitrile and nitromethane solutions when 15C5 is present at 298 K Sol . K E. ' AH" 45* 110* AN (2.5:0.4)x103 4.83:0.01 4.2410.01 -24.3i'0.3 11.4510.09 NM (1514))(10‘ 4.98:0.09 4.3910.09 -20.110.2 10.410.2 a. E" AH*, and AG", in units of kcal°mol": AS" in the units of cal'mole'1'K": b. k: the decomplexation rate constant kd corresponding to the associative-dissociative mechanism in acetonitrile solutions with the units of s‘: or the exchange reaction rate constant.kq of the bimolecular exchange mechanism in nitromethane solutions with the units of s 1°"M 0. AN, NM are abbreviations for acetonitrile and nitromethane respectively. 189 Table 41. Complexations of some ligands with neutral organic molecules in benzene at 298 K Host Guest Association Guest Association Constant Constant (m. f") (m. f") 1505 MeCN Km=4 . 5:0. 2 MeNOz Km=5. 210. 9 815C5 MeCN K1:1=5 o 110 o 6 MeNOz K1:1=2 0 5:0 0 6 1806 MeCN Km=1212 MeNOZ Km=15i2 K1=2=2.9i0.5 K1:2=16i3 2107 MeCN Km=l3il TG MeCN Km=4.3:0.2 MeNOZ Km=5.010.5 90 149.011 Km=7 . 1:0 . 2 Reference 100 TC: tetraglyme: PG: pentaglyme. 0-00‘ numb, “I o . Complexedltb‘ U1SCShAI A run-14:04.0" -.50- . Complexed 11:0, 171505 hu 3‘ / Ga - . a 100.1 a H I ...4 .c “ -1.50- .-I 0 O «1 01-1 3 .c: -2.00- O h | d .... 1-1 , -2.50- ‘0 -3.00-1 -30” ‘TrI'U'I'I'T'rfI'T 230. 240. 250. 200. 270. 280. 290. 300. 310. 320. T (K) Figure 33. Li-7 chemical shifts of the uncomplexed LiClO, and the complexed LiClO, by 15C5 as functions of temperature in acetonitrile and nitromethane solutions the total LiClO, concentration: 0.05M 191 2.. O Fmttb‘ilfl O euphdttb‘ly‘lSCShll d 1 1 4 ’7 2.0 o T * 0 ‘ m 1 V a 1.4m 4 fl 00-. 4 1 «H g 1.11 1 O 'H 1 ‘ 13 a to U T I r V f to V t I f f r '3 O." m 0 H 0 W o rmltb‘ III q I Coophxedltb‘iyficsull 5 u. ‘ 00 ¢ 4 N 5* ~ 10¢ { ’3 ¢ J 54 } 2.4+ J V 4 1 I: H 11‘ J ‘ T 2.0 . r r r 2.0 r r . T l/T, T: the absolute tenperature K Figure 34. The relaxation rates of Li-7 of the unconplexed LiClO‘ and the conplexed LiClO‘ by 15C5 as functions of the reciprocal temperature in acetonitrile and nitromethane solutions the total LiClO‘ concentration: 0.05M 192 .cowusdou «Aduuwcoumoo 5 33 + .083 now cred} .m> profit} .3 «use: trad} .38... c .381 o IIUUIIIUIU IIIIUIIUI' IIUUIIIIUU :8..- .. .388 u 893' e l8...“- ‘Lmh/t 193 nowusdou mnanuoEOHUMG 5 33 + .033 you trod} .m> #73:} .3 0.53m trad} OO— 03— n‘ a? _ 90' Oflp .‘ a. A!“ 00— Ofl— n‘ 00 : —|LVL . _ _ . _ . 0 _ . _ _ . _ . w u _ . L . _ . _ . _ . o a" u [#938 n/H I H I I .Iflxfl— .. I8+H :8:- cn 28:. a 2.81 c “13.93 00— ON— a! 0' . OG— OR. Al 60 . AUG 00— 08— A' a? E . — _ n — . 0 E n — — n h n 0 — . — - — b — . — . ”0 II r I r I ‘ J I } 3+8 - - 92W— : r nififl 331-” 23!.” :fiio 3i ‘IJ'IJJ/I 12.000- . Lic10‘(o.1ozo u) + 15¢5(0.0506 x) . L1c10‘(o.1039 n) + 15C5(0.0350 x) 11.000- A Lic10‘(o.1ozo n) + 15C5(0.0720 u) T 2 10.000- -H «U . 0 f: 9.000- .... 5 -+ 2 8.000-* 0 d a " 7.ooo- : q :5 6.000- ’ \ g . 5 5.000- 1 4.000- 3.000 I l I ' I I I l r l j 0.0031 0.0033 0.0035 0.0037 0.0039 0.0041 l/T, T: the absolute tenperature K Figure 37. In (1/1) against l/T for the system LiClO‘-+ 1565 in acetonitrile solutions 195 12.0- . LiClO‘(0.0521 u) + 1505(0.0216 n) g 0 LiClO‘(0.0465 n) + 15C5(0.0366 n) a LiClO‘(0.0334 x) + 1505(0.0277 u) ”o_ . L'iC10‘(0.0766 x) + 1505(0.0175 u) 0 ‘1 I .... H ‘fl101 0 H 0d d H 5 9.0- 0 I ¢ 1 3 .. 800‘ b I? a 7.0~ fl . H 0.0- 5.0 0.0030 ' 0.0532 - 0.01034 ' 0.0030 t 0003;005:401 0.0342 ' 1/T, T: the absolute tenperature K Figure 38. In (1/1) against 1/T for the system LiClO‘-+ 15C5 in nitromethane solutions 196 10.0001 9.000 - lnk‘, 45°00 r I ' I ' I ' I T I 0.0031 0.0033 0.0035 0.0037 0.0030 0.0041 l/T, T: K Figure 39. ln 1:, against l/T for the system LiClO‘ + 1505 in acetonitrile solutions 1“ k1 13.0- 12.5- 12.04 11.51 11.0- 10.5- 10.0-* 9.5 «- 197 0.0030 ' 0.0032 ' 0.0034 3.0330 7.0030 - 0.0040 0004: ' 1/1', 1': K Figure 40. ln 1:, against 1/‘1‘ for the system LiClO‘ + 15C5 in nitromethane solutions APPENDICES 199 Appendix A DATA TRANSFER Following the next few steps to transfer a data file from the Bruker-180 spectrometer to the VAX system: 1. On the VAX system, open a file that the data are to be transferred: (T)"’ RUN [ZJGETNMR (R)* GETNMR-Version 20-Apr-198‘7 (R) TARGET FILE: (T)TEST.DAT 2. 0n Bruker-180, run the data transfer program: (T) RUN NTCTDL (R) DATA-TRANSFER PROGRAM VERSION #10903 (R) COMMAND: (R) BI,BO,CP,AP,AR,KB,LP,LR,MO,TL,TT? (T) BO (R) WHAT FORMAT(A=ASCII, B=BINAR)? (T) A (R) WHAT PARITY(E, O, M, N)? (T) N (R) MAXIMUM RECORD LENGTH = 64 (Return) (R) PROMPT = (T)12 (R) ENTER TERMINAL MODE (Y, N)? 200 (T) N(at this point, the data are being transferred) 3. 0n the VAX system, type 'S' to exit the file TEST.DAT. Now the transfer is finished, and the data are stored in a file named TEST.DAT on the VAX system. 4. 0n Bruker-180, exit the data transfer program. (R) COMMAND: (R) BI,BO,CP,AP,AR,KB,LP,LR,MO,TL,TT? (Y) MO Data transfer is finished. *. Throughout the appendix sections, (T) and (R) are used in front of each Of the steps to indicate the strings that immediately follow (T) and (R) to be typed(T) by users or to be the response(R) from the computers, when describing the computer Operational procedures. 201 Appendix B GETNHR.FOR PROGRAM GETNHR C 0 Title: GETNMR.FOR - Get a data set from the Nicolet 180 C C Author: T V Atkinson c Chemistry Dept. c Michigan State University C East Lansing, MI 1.8824 C C DATE: 16-APR-1987 C C PARAMETER (HAXREC880) ! Haxiuun length record C TNTEGER*2 1088(6) I 010 return status block TNTEGER*2 LUNOUT l Unit to receive output IlTEGER'Z lOFUNC l OR'ED lOFUNCTlON CODE TNTECER'Z LUNTI I Unit for TT: iNTEGER‘Z NBYTES l Nulber of bytes in record llTEGER*4 STATUS I 010 status return llTEGER'Z PLCHAN ! 010 Channel C LOGICAL*1 STRING(BO) ! input string buffer LOGICAL*1 OUTKIN(4) ! Extension for KINFIT file L06!CAL*1 IHRREC(HAXREC) ! Buffer to receive info from ITCTBO L06!CAL*1 PBUFF(1) l Prompt for NICTBO C CHARACTER LUNNHR*Z/'TT'/ ! Device to NIC180 C [ICLLDE 'mooen' INCLUDE '(SSSDEF)' INTEGER". SYSSOIW , SYSSASS 1 GM , SYSSDASSGN 50 8510 8000 202 DATA PBUFF/OiSI, LUNTTISI, LUNOUT/1/ URITE (LUNTI,8500) FCRHAT (' GETNHR - Version 20-APR-1987') svarus a svssnssxcu< LUNNMR, PLCHAN,, ) ! Get a channel. 1F ( STATUS .NE. 1 ) THEN I if failure, then give the TYPE 1001 1 user some idea what it is. CALL LIBSSTCNAL( XVAL( STATUS )) I Give the VHS official reason STOP ! and bail out. END 1F Get file name iOFUNCs(IosN_NOEcu0 .OR. IOS_READPROMPT) URiTE (Luurx,as10) rerun! ('ITARGET FILE: ') READ (LUNTI,8000,ERR=50,ENO=999) Lsrnuc,5131uc FORMAT (0,80A1) s:n1uc . 0 open (UNIT8LUNOUT,NAHESSTRING,TYPEI'NEH',ERR=50, 1 mausecoumou'usm Get next record Prompt with PBUFF, read response. 2133 100 NDYTES 8 HAXREC STATUS - svssoxow< XVAL(3), XVAL(PLCNAN),XVAL(iOFUNC), 1 XREF(TOSB),,, XREF(NHRREC), XVAL(NBYTES),,, PDUFF, XVAL(1)) I Read a byte from digitizer. IF ( STATUS .NE. 1 ) THEN I if failure, then give the TYPE 1003 I user some idea what it is. CALL LIBSSIGNAL( XVAL( STATUS )) I Give the VHS official reason GOTO 200 END 1F NBYTES 8 [088(2) IF ( unanac<1> .50. 's' ) 0010 200 NRlTE (LUNOUT,8520) (NHRREC(K),K81,HBYTES) 8520 FORMAT (80A1) GOTO 100 C C Invoke the system service SDASSGN to deassign the channel to the C 200 STATUS - SYSSDASSGN< XVAL< PLCHAN )) I De-assign channel. IF ( STATUS .NE. 1 ) THEN I If failure, then give the TYPE 1000,5TATUS I user some idea what it is. CALL LIBSSIGNAL( XVAL( STATUS )) I Give the VHS official reason STOP I and bail out. END IF 999 STW 'GETNHR ' C 1000 FORMAT (//,' *** Error de-assigning the Nicolet 180: ***') 1001 FORHAT (l/,' **' Error assigning the Nicolet 180:') 1003 FORHAT (//,' *** Error in prompted-read from Nicolet 180:') 1006 FORHAT (' iOSBs',617) END 204 Appendix c Data Transformation A data file can be transformed into a KINFIT workable format by doing the following: (T) RUN [Z]NIC180 (R) NIC180 (Version:21-Jan-1986) (R) Should the output be in KINFIT Format?[Y/N] (T)Y (R) Input File: (T)TEST.DAT (R) NSKIP,XVAR,YVAR:(T)0,0.000001,l (R) XINIT,XDELTA[D:O,1]: (T)-21.000,9.800 (R) 88 points are transformed.(Transformation is done.) When running this program, a few parameters need to be provided by users: NSKIP is the number of data from the input data file to be skipped: XVAR and YVAR are the variances Of data in x and y: XINIT and XDELTA are the initial value Of the data file and the interval between each data point respectively in frequency(hz). In this example, no points(0) were skipped and the variances in x and y are 0.000001 and 1 respectively, the frequency for the first data point of the file was -21.000 hz and the interval between each point was 9.800 hz. 205 Appendix D NIC180--Data formatting programs I NIC180.COH - Build NIC180, a program for reformatting NMR data I T V Atkinson I Department of Chemistry I Hichigan State University I East Lansing, HI (.8821. Date: 03-JUL-85 1 COMFORT :" ILIST/M014 LTMKOPT :3! [MAP DELETE DTRVMS.LTS;*,DTRVMS.OBJ;* FUTTRAM'WT' DTRVMS DELETE M10180.LIS;',MTC180.00J;* S FORTRAM'COMPLTST' M1C180 5 DELETE MTC1OD.MAP;*,MIC180.EXE;* 5 LIMK'LTMKOPT' MICTGO,DIRVMS ”flflflfiflflflfiflflfiflfififlfifi PROGRAM M1C180 Title: NICTBOJTN - Process data from Nicolet 180 NHR Author: T V Atkinson Chemistry Dept. Hichigan State University East Lansing, HI 68826 DATE: 18‘JUL-85 00006000000 206 ['1 C C C variable definitions C LOGICAL*1 STRINGIBO) I Input string buffer LOGICAL'I OUTKIN(4) I Extension for KINFIT file LOGICAL*1 OUTEXTI‘) I Extention for HULPLT file LNICAL" INDDIR LOGICAL'I BLANK LOGICAL‘I ICR LOGICAL'I ATSIGN LOGICAL‘T PERIw LOGICAL'I KINFIT LOGICAL*1 COHHA LOGICAL*1 ICY I ASCII "Y" LOGICAL'I ICYLC I ASCII "y" LOGICAL'I IGNORE I Flag for ignore this line LOGICAL'I DOLLAR I ASCII “S“ C INTEGER‘Z NPLINE I Number of data points per line INTEGER‘Z NPOINT I Number of points loaded INTEGER*2 HAXPNT I Haximua number of points allowed C REAL'A YDATA(1000) I Array to hold y data C DATA LUNTI,LUNIN,LUNOUT,LUNDIR/S,1,2,3/ DATA BLANK/“ADI, ICRI'ISI, ATSIGN/IN DATA OUTKINI'K','I','N',' 'l, 0UTEXT/‘N','H','R',' '/ DATA PERIOD/'.'l, ICYI'Y'I, ICYLC/‘y'l DATA COHMA/‘,'I.DOLLAR/'S'/ DATA NPLINE/8/,HAXPNTIIOOOI C C ..................................................................... c Entry Point C ..................................................................... C NRITE (LUNTI,8500) C 207 100 URITE (LUMT1,8510) READ (LUMTI,8000,ERR8320,END=320) LSTRMG,STRTMG KINFIT 3 (STRING(1) .EO. ICY) .OR. (STRIMG(1) .EO. ICYLC) C URTTE (LUMTI,8530) READ (LUNTI,8000,ERR=320,EMD=320) LSTRHG,STRTNG IF (.MOT. KINFIT) GO TO 110 C URITE (LUNTI,8560) READ (LUNTT,8550,Euo-320) NSKIP,XVAR,YVAR IF (usurp .LT. 0) usxxp = o INCR1 . nser + 1 INCRZ . 2*INCR1 11o CONTINUE 120 TMDDIR I STRING(1) .EO. ATSTGN IF (.MOT.IMDDIR) GO TO 140 CALL DTRVMS(0,LUMDIR,LUMEL,STRTMG(2),LSTRNG-1,LDEVM,LVERS,IERR) 1F (TERR.ME.O) GO TO 310 Process the next file 130 CALL DIRVMS (1,LUMDTR,LUMEL,STRTMG,LSTRMG,LDEVM,LVERS,IERR) If (IERR.EO.-1) 00 TO 230 If (IERR.GT.O) 00 To 310 If (INDDIR) NRITE (LUNTI,8560) (STRING(K),K-1,LSTRNG) 140 NRITE (LUNTI,857D) 208 READ (LUMTI,8020,EMD'320) XIMIT,XDELTA IF (XDELTA .EO. 0.0) XDELTA 8 1.0 150 STRIMGILSTRMG+1) ' 0 OPEN (UMITILUMIM,MAME8$TRING,TYPEI'OLD',ERR8210, 1 CARRIAGECOMTROLI'LIST',READOMLY) K1 I -MPLIME + 1 C Parse the file spec DO 160 I=1,LSTRNG 160 IF (STRINGII) .EO. PERIOD) IPER = I 11 I IPER + 1 12 8 IPER + 3 J 3 0 Put in “.NHR“ IF (KINFIT) GO TO 180 00 170 I=I1,I2 J I J + 1 170 STRIMGII) ‘ OUTEXT(J) GOTO 200 Put in ".KIN“ 180 D0 190 I=11,12 J I J 0 1 190 STRIMG(I) 3 OUTKIM(J) 200 OPEM (UMIT8LUMOUT,MAME88TRING,TYPE='MEH',ERRIZZO, 1 CARRIAGECOMTROLI'LIST') Process the next record 261 260 270 265 READ (LUNIN,8000,END=300) LSTRN,STRING Discard null lines IGNORE I .FALSE. 00 2‘1 I=1,LSTRN IF (STRING(I) .EO. DOLLAR) IGNORE 8 .TRUE. CONTINUE IF (IGNORE) GOTO 260 IF (LSTRN .LE. 0) GOTO 240 Convert extraneous to blank DO 250 I81,80 IF (STRING(I) .EO. ICR) STRING(I) = BLANK Find end of line DO 260 I=1,80 NCHAR 8 80 - I o 1 IF (STRING(NCHAR) .NE. BLANK) GO TO 270 CONTINUE Convert spaces to commas 00 265 I-1,NCHAR IF (STRING(I) .EO. BLANK) STRING(I) CONTINUE COMMA Decode and Load into YDATA K1 8 K1 f NPLINE IF (K1 .GT. MAXPNT) GOTO 299 NPOINT I MINO( (K1 + NPLINE - 1), MAXPNT) DECODE (NCNAR,8020,STRING) (YDATAIK),K=K1,NPOINT) GOTO 260 Data load terminated due to overflow URITE (LUNTI,8685) 1310 280 1350 210 End of input file CLOSE (UNITsLUNIN) URITE (LUNTI,8680) NPOINT IF (KINFIT) GO TO 280 DO 1310 I81,NPOINT X1 8 XINIT f I’XDELTA HRITE (LUNOUT,8620) X1,YDATA(I) 0010 400 00 1350 I81,NPOINT,INCR2 12 - 1 + INCR1 x1 . x1u11 + 1*XDELTA x2 . x1u11 + I2‘XDELTA UNITE (LUNOUT,8630) X1,XVAR,YDATA(I),YVAR,X2,XVAR,YDATA(IZ) 1,YVAR CONTINUE CLOSE (UNIT‘LUNOUT) IF (INDDIR) GOTO 130 GOTO 100 End of all files 211 310 CLOSE (UNIT‘LUNDIR) GOTO 100 C C ..................................................................... C C STOP C C ..................................................................... C 320 STOP 'NIC180' C C ..................................................................... C C Error Handlers C C ..................................................................... C 210 , HRITE (LUNTI,8580) (STRING(I),I=1,LSTRNG) GOTO 310 220 URITE (LUNTI,8590) (STRING(I),I=1,LSTRNG) GOTO 310 230 NRITE (LUNTI,8600) GO TO 310 C c ........................................................................... C C Formats C C ........................................................................... C 8000 FORMAT (0,80A1) 8020 FORMAT (10F16.0) 8500 FORMAT (ll' NIC180 (Version: 21-JAN-1986I') 8510 FORMAT ('SShould the output be in KINFIT format? [Y/Ni') 8530 FORMAT('SINPUT FILE: ') 8560 FORMAT ('SNSKIP,XVAR,YVAR: ') 8550 FORMAT (I8,2E15.0) 8560 FORMAT (1X,8OA1) 8570 FORMAT ('SXINIT,XDELTA [0: 0,1]: ') 8580 FORMAT(' Can"t open input file: ',80A1) 8590 FORMAT(' Can"t open output file: ',80A1) 8600 FORMAT (' Error in DIRVMS') 212 FORMAT ('RD ',F10.3,','F10.0) FmMAT (4(F10.3,',',E10.3,',')) FORMAT (' Nmber of points loaded: ',I8) FORMAT (' Data load trmcated - Too many points: ') END 213 Appendix E EXAMPLES OF DATA FILES 214 E.1 TEST.DAT 10588 11022 11388 11613 11738 11933 12367 13071 13916 16789 15650 16669 17268 18072 19079 20322 21752 23296 26888 26631 27906 29511 31528 36056 36991 60311 66152 68586 53553 59066 65161 71950 79385 87556 96737 107105 118731 131830 166762 163635 182572 203707 226285 266763 258716 256766 260785 216396 190559 167651 167892 131637 117685 106130 96050 86965 78831 71677 65350 59705 56735 50395 66571 63188 60216 37566 35105 32803 30722 28868 27111 25555 26282 23267 22200 20983 19602 18133 16677 15670 16780 16559 16399 13918 13100 12190 11397 10815 This is the digitized format of the intensity of an NMR signal of the species undergoing the exchange reactions, transferred from the Bruker-180 spectrometer. In order to perform KINFIT, this data file has to be rewritten into a KINFIT readable file by adding the frequency intervals between each data point, and variances in frequency and intensity. This is done by running NIC180 program described in Appendix C. The result of this data transformation is shown in TEST.KIN in the next section. 215 E.2 TEST.KIN -7.320, 0.100E-05, 10588.000, 0.100E+01, -9.760, 0.100E-05, 11022.000, 0. 100E+01, -12.200, 0.100E-05, 11388.000, D.100E+01, -16.660, 0.100E-05, 11613.000, 0. 100E+01, -17.080, 0.100E-05, 11738.000, 0.100E+01, -19.520, 0.1005-05, 11933.000, 0. 100E+01, -21.960, 0.100E-05, 12367.000, 0.100E+01, -26.600, 0.100E-05, 13071.000, 0. 100E+01, -26.860, 0.100E-05, 13916.000, O.100E+01, -29.280, 0.100E-05, 16789.000, 0. 100E+01, -31.720, 0.100E-05, 15650.000, 0.100E+01, -36.160, 0.100E-05, 16669.000, 0. 100E+01, -36.600, 0.100E-05, 17268.000, 0.100E+01, ~39.06D, 0.1ODE-05, 18072.000, 0. 100E+01, -61.680, 0.1005-05, 19079.000, 0.100E+01, -63.920,.0.100E-05, 20322.000, 0. 100E+01, -66.360, 0.100E-05, 21752.000, 0.100E+01, -68.800, 0.100E-05, 23296.000, 0. 100E+01, -51.260, 0.100E-05, 26888.000, 0.100E+01, -53.680, 0.100E-05, 26631.000, 0. 100E+01, -56.120, 0.100E-05, 27906.000, 0.100E+01, -58.560, 0.1005-05, 29511.000, 0. IDOESOI, -61.000, 0.100E-05, 31528.000, 0.100E+01, -63.660, 0.100E-05, 36056.000, 0. 100E+01, -65.880, 0.100E-05, 36991.000, 0.100E+01, -68.320, 0.100E-05, 60311.000, 0. 100E+01, -70.760, 0.100E-05, 66152.000, 0.100E+01, -73.200, 0.100E-05, 68586.000, 0. 100E+01, -75.660, 0.100E-05, 53553.000, O.100E+01, -78.080, 0.100E-05, 59066.000, 0. 100E+01, -80.520, 0.100E-05, 65161.000, 0.100E+01, -82.960, 0.100E-05, 71950.000, 0. 100E+01, -85.600, 0.100E-05, 79385.000, 0.100E+01, -87.860, 0.1005-05, 87556.000, 0. 100E+01, -90.280, 0.100E-05, 96737.000, 0.100E+01, -92.720, 0.100E-05,107105.000, 0. 100E+01, -95.160, 0.100E-05,118731.000, 0.100E+01, -97.600, 0.100E-05,131830.000, 0. 100E+01, -100.060, 0.100E-05,166762.000, 0.1OOE+01, -102.680, 0.100E-05,163635.000, 0. 221GB 100E+01, -106.920, 0.100E-05,182572.000, O.100E+01, -107.360, 0.100E-05,203707.000, 100E+01, -109.800, 0.100E-05,226285.000, O.100E+01, -112.260, O.100E-05,266763.000, 100E+01, -116.680, 0.100E-05,258716.000, 0.100E+01, -117.120, 0.100E-05,256766.000, 100E+01, -119.560, 0.100E-05,260785.000, O.IOOE+01, -122.000, 0.100E-05,216396.000, 100E+01, -126.660, 0.100E-05,190559.000, O.100E+01, -126.880, 0.100E-05,167651.000, 100E+01, -129.320, 0.100E-05,167892.000, 0.100E+01, -131.760, 0.1006-05,131637.000, 100E+01, -136.200, 0.100E-05,117685.000, 0.100E+01, -136.660, 0.100E-05,106130.000, 100E+01, °139.080, 0.100E-05, 96050.000, 0.100E+01, -161.520, 0.1006-05, 86965.000, 100E+01, -163.960, 0.100E-05, 78831.000, 0.1OOE+01, -166.600, 0.100E-05, 71677.000, 100E+01, -168.860, 0.1006-05, 65350.000, 0.IOOE+01, -151.280, 0.100E-05, 59705.000, 100E+01, -153.720, 0.100E-05, 56735.000, 0.100E+01, -156.160, 0.100E-05, 50395.000, 100E+o1, -158.600, 0.100E-05, 66571.000, 0.100E+01, -161.060, 0.100E-05, 63188.000, 100E+01, ' -163.680, 0.1006-05, 60216.000, 0.100E+01, ~165.920, 0.100E-05, 37566.000, 100E+01, -168.360, 0.100E-05, 35105.000, 0.IOOE+01, -170.800, 0.100E-05, 32803.000, 100E+01, -173.240, 0.100E-os, 30722.000, 0.100E+01, -175.aao, 0.100E-05, 28868.000, 100E+01, -178.120, 0.1005-05, 27111.000, 0.IDDE+01, -180.560, 0.1006-05, 25555.000, 100E+01, -183.000, 0.100E-05, 26282.000, 0.IOOE+01, -185.640, 0.1006-05, 23267.000, 1006+01, -187.880, 0.100E°05, 22200.000, 0.100E+01, -190.320, 0.100E-05, 20983.000, 100E+01, -192.760, 0.1006-05, 19602.000, 0.1005+o1, -195.200, 0.1006-05, 18133.000, 100E+01, -197.660, 0.100E-05, 16677.000, 0.100E+01, -200.080, 0.100E-05, 15670.000, 100E+01, -202.520, 0.100E-05, 16780.000, 0.100E+01, -206.960, 0.100E-05, 16559.000, 100E+01, 217 -207.600, 0.100E~os, 14399.000, 0.100E+01, -209.860, 0.100E-os, 13913.000, 0. 100E+01, -212.zao, 0.100E-05, 13100.000, 0.100E+o1, -214.720, 0.100E-os, 12190.000, 0. 100E+01, ~217.160, 0.100E-05, 11397.000, 0.100E+01, -219.600, 0.100E-os, 10815.000, 0. 100E+01, For the full-line-shape-analysis by KINFIT, additional information needs to be supplied, and the name of the data file has to be changed to TESTK.DAT. See the next section. E . 3 TBSTK. DAT ”I 020' l , , , 8, .00001 2JL£3 LISN231N.DAT. 0.0262M LITPB/0.0066M 15C5/AN AT 299K. .7576, .0215, -791.268, .2626,.0169, °656.366, 250.0E-6, 67.1239 0.308939E+08, 0.397078E+06, -0.636963E-01, -0.806E+02, 0.116603E-02 -7.320, 100E+01, -12.200, 100E+01, -17.080, 100E+01, -21.960, 1006+01, -26.860, 100E+01, -31.720, 100E+01, -36.600, 100E§01, -61.680, 100E+01, -66.360, 1005+01, -51.260, 100E+01, -56.120, 100E+01, -61.000, 100E+01, -65.880, 100E+01, -7D.760, IDOE+DI, —75.660, IODE+01, -80.520, 100E+DI, -85.600, 0.100E-05, 0.1006-05, 0.100E-05, 0.100E-05, 0.100E-05, 0.1005-05, 0.100E-os, 0.100E-05, 0.100E-05, 0.1006-05, 0.100E-05, 0.100E-05, 0.100E-05, 0.1005-05, 0.100E-05, 0.100E-05, 0.100E-05, 10588.000, 0.100E+01, -9.760, 0.100E-05, 11022.000, 0.100E+01, -16.660, 0.100E-05, 11613.000, 0.100E+01, -19.520, 0.100E-05, 11933.000, 0.1OOE+O1, -26.600, 0.100E-05, 13071.000, 0.100E+01, -29.280, 0.100E-05, 16789.000, 0.100E+01, -36.160, 0.1ODE-05, 16669.000, 0.100E+01, -39.060, 0.100E-05, 18072.000, 0.100E+01, -63.920, 0.100E-05, 20322.000, 0.100E+01, -68.800, 0.100E-05, 23296.000, 0.100E+01, -53.680, 0.100E-05, 26631.000, 0.100E+01, -58.560, 0.100E-05, 29511.000, 0.100E+01, -63.660, 0.100E-05, 36056.000, 0.100E+01, -68.320, 0.100E-05, 60311.000, 0.100E+01, -73.200, 0.100E-05, 68586.000, 0.100E+01, -78.080, 0.100E-05, 59066.000, 0.100E+01, -82.960, 0.100E-05, 71950.000, 0.100E+01, -87.860, 0.100E-05, 87556.000, 0. 100E+01, -90.280, 100E+01, -95.160, 100E+01, -100.060, 100E+01, -106.920, IDDESDI, -109.800, 100E+01, -116.680, 100E+01, °119.560, 100E+01, -126.660, 100E+01, -129.320, 100E+01, -136.200, 1OOE+DI, -139.080, 100E+01, ~163.960, 100E+01, —168.860, 100E+01, -153.720, 100E+01, -158.600, 100E+01, -163.680, 100E+01, ~168.360, 1005+01, -173.260, 100E+01, -178.120, 100E+01, -183.000, 100E+01, ~187.880, 100E+01, 0.100E-05, 96737.000, 0.100E-05,118731.000, 0.1005-05,166762.000, 0.100E-05,182572.000, 0.100E-05,226285.000, 0.100E-05,258716.000, 0.100E-05,260785.000, D.100E-05,190559.000, 0.100E-05,167892.000, 0.100E-05,117685.000, 0.100E-05, 0.100E-05, 0.100E-05, 0.100E-05, 0.100E-05, 0.1008-05, 0.100E-05, 0.100E'05, 0.100E-05, 0.100E-05, 0.100E'05, 96050.000, 78831.000, 65350.000, 56735.000, 66571.000, 60216.000, 35105.000, 30722.000, 27111.000, 26282.000, 22200.000, 219 o.1ooe+o1, -92.72o, 0.100E+01, -97.600, 0.100E+01, -102.aso, o.1oos+01, -107.360, o.1ooe+01, -112.2ao, 0.100E+o1, -117.120, 0.IOOE+01, -122.ooo, 0.1OOE+01, -126.880, 0.100E+o1, -131.760, 0.100E+01, -136.660, 0.100E+01, -141.520, O.IOOE+01, -166.600, 0.100E+01, -151.zso, 0.100E+01, -156.160, 0.100E+01, ~161.060, 0.100E+01, -165.920, 0.1OOE+01, -170.aoo, 0.100E+o1, -175.eao, 0.1OOE+01, -180.560, 0.100E+01, -185.660, 0.100E+01, -19o.320, 0.100E-05,107105.000, 0.100E-05,131830.000, 0.100E-05,163635.000, 0.100E-05,203707.000, 0.100E-05,266763.000, 0.100E-05,256766.000, 0.100E-05,216396.000, 0.100E-05,167651.000, 0.100E-05,131637.000, 0.100E-05,106130.000, 0.100E-05, 86965.000, 0.100E-05, 71677.000, 0.100e-05, 59705.000, 0.100E-05, 50395.000, 0.100E-05, 63188.000, 0.100E-05, 37566.000, 0.100E-05, 32803.000, 0.100E-os, 28868.000, 0.100E-os, 25555.000, 0.100E-05, 23267.000, 0.1ODE-05, 20983.000, 220 -192.750, 0.100E-os, 19602.000, 0.100E+01, -195.2oo, 0.100E-05, 18133.000, 0. Tammn . -197.660, 0.100E-05, 16677.000, 0.100901, -zoo.oso, 0.100E-05, 1500.000, 0. 1mmwn -202.520, 0.100E-05, 14730.000, o.1ooe+o1, -zos.9ao, 0.100E-os, 14559.000, 0. 1OOE+01, -207.£oo, 0.100E-os, 14399.000, 0.100E+01, ~209.860, 0.100E-05, 13913.000, 0. 100E+01, -212.zso, 0.100E-os, 13100.000, 0.1OOE+01, -214.720, 0.100E-os, 12190.000, 0. 100E+01, -217.160, 0.1OOE-os, 11397.000, 0.100E+o1, -219.600, 0.100E-05, 10815.000, 0. 100E+o1, This is the final complete version of the data file that is to be fitted to a two-site exchange equation by running KINFIT program to derive the best estimate of 1 along with some other parameters. The top line is equivalent to the control card given in the Older version of KINFIT. It contains information such as the number of points(88), the maximum number of iterations allowed before convergence(20), the number of constants that are to be read for the equation to fit the data(8), the maximum value of Aparameter/parameter for convergence(0.00001), Aparameter is the change in the parameter from one iteration to the next). The second line is the title of the file, which can be any information desired by users. The third and the last line are the constants and the estimates of the parameters to be fitted, the orders of which are in accordance with that given in NMRZsiteb subroutine(see Appendix H). Hflflflflflflflflflflflflflflflflfiflfifl S S S S S S S S S S 221 Appendix F KINBLD.COH I I I KINFIT:KIN8LD.COM - Submit a batch job to build a KINFIT prog. I I T V Atkinson I Department of Chemistry I Michigan State University I East Lansing, MI 68826 I Date: 08-MAY-1987 I I HERE :II 'FSLOGICAL("SYS$DISK")"FSDIRECTORY()' SET DEF 'HERE' JNAME ="KIN_“+F$EXTRACT(0,5,P1) LENFN I FSLOCATEI“.',P1) FILNAME I FSEXTRACT(0,LENFN,P1) FM 8 FILNAME SET MESSAGE/NOID/NOFACILITY/NOSEV/NOTEXT DELETE 'FILNAME' .LOG;*, 'FILNAME' .J08;* SET MESSAGE/ID/FACILITY/SEV/TEXT OPEN/HRITE TEMPFILE 'FILNAME'.J08 HRITE TEMPFILE “S I Temporary file for building KINFIT“ NRITE TEMPFILE "S SET DEF “,HERE NRITE TEMPFILE "S SET MESSAGE/NOID/NOFACILITY/NOSEV/NOTEXT' URITE TEMPFILE "S DELETE ',FN,".OBJ;*,",FN,'.EXE;*,',FN,'.LIS;*" NRITE TEMPFILE "S SET MESSAGE/ID/FACILITY/SEV/TEXT NRITE TEMPFILE ”S FORTRAN/LIST ",P1 NRITE TEMPFILE “S LINK/HAPI“,FN,'/EXE-“,FN," KINFIT:VAXKINFIT,',HERE,FN CLOSE TEMPFILE SUBMIT/OUEUE-KINFITO/LOG-'HERE"FILNAME'.LOG/NOPRINTER/NOTIFY/NAMEI'JNAME'- 'FILNAME'.J08 ”Hflflflfiflflflflflfififlflfifl”Uflflflfififlflfl 222 Appendix G KINRUN.COH I KINFIT:KINRUN.COM - Submit a batch job to run a KINFIT prog. I T V Atkinson I Department of Chemistry I Michigan State University I East Lansing, MI 68826 I Date: 31-SEP'86 1 Usage. I I S KINRUN eqn dataset I I where "eqn' is the name of the EON to be used, and 'dataset“ is I the name of the file containing the data set. 1 I HERE :2 ‘FSLOGICAL(”SYSSDISK”)"FSDIRECTORY()' SET DEF 'HERE' JNAME I“KIN_'+FSEXTRACT(0,5,P1) LENFN . FSLOCATE('.",P1) LENFN1 - FSLOCATEI'.",P3) EONNAME . FSEXTRACTIO,LENFN,P1) S DATNAME 8 FSEXTRACT(0,LENFN,P2) S SET MESSAGE/NOID/NOFACILITY/NOSEV/NOTEXT S DELETE 'DATNAME'.J08;' S SET MESSAGE/ID/FACILITY/SEV/TEXT S OPEN/UNITE TEMPFILE 'DATNAME'.J08 S NRITE TEMPFILE "S I Temporary file for doing a KINFIT run“ 223 S RITE TEMPFILE “S SET DEF “,HERE S RITE TEMPFILE "S ASSIGN ",P2,".DAT FROM" S RITE TEMPFILE “S ASSIGN “,P2,".REP FROOZ" S IF LENFN1 .NE. 0 THEN S RITE TEMPFILE "S ASSIGN “,P3,".DAT FOR060" S RITE TEMPFILE "S RUN “,P1 S CLOSE TERFILE S SlJOMIT/WEUEBKINFITOILOG8' HERE ' 'DATNAME' .Lm/NWRINTER/NOTIFY/NAMES'JNAME ' - 'DATNAIE'JG 224 Appendix H SUBROUTINE EQN-NHRZSITE.FOR SUBROUTINE EON nonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn NMRZSITE.FOR - NMR THO-SITE EXCHANGE UITH CORRECTION FOR LINE BROADENING, DELAY TIME AND ZERO-ORDER DEPHASING. PARAMETERS 0(1) = K (INTENSITY . UNITLESS) U(2) = 8 (BASELINE INTENSITY . UNITLESS) U(3) = THETA (ZERO ORDER PHASE CORRECTION . RAD U(6) = DELTAU (FRED. CORR.'2(PI)(DELTANU) . RAD. U(5) = TAU (EXCHANGE RATE . SEC.) CONSTANTS CONST(1) = PA (POP. OF FREE SITE . UNITLESS) CONST(2) 8 T2A (RELAXATION TIME . SEC./RAD.) CONST(3) = HA (NA=2(PI)(NUA) . RAD./SEC.) CONST(6) = P8 (POP. OF COMPLEXED SITE . UNITLE CONST(5) = T28 (RELAXATION TIME . SEC./RAD.) CONST(6) = N8 (U882(PI)(NUB) . RAD./SEC.) nonnnnn 225 CONST(7) 8 DE (DELAY TIME . SEC.) CONST(8) = LB (LINE BROAD.'(PI)(LB(HZ)) . RAD. IMPLICIT REAL*8(A'H,O°Z) IMPLICIT INTEGER*6(I-N) INCLUDE 'KINFIT:KINFITCOM.FOR/LIST' INCLUDE 'KINFIT:KINEONCOM.FOR/LIST' COMPLEX‘16 ALPHA,ALPHB,XLAMA,XLAMB,C1,C2,XS,BRUCE,ALEX,AL,FRED ITYPE I 5: Initial call. N0 input has taken place 1 CONTINUE NRITE (LUNOUT,8500) I Log the ID of this routine 8500 FORMAT (' ***EON: CEM 671 Method 2 (06-SEP-85)***') RETURN ITYPE I 6: Control card #1 and CONST have been input 7 CONTINUE NOUNKIS NOVARIZ 1002 1001 1000 226 RETURN ITYPE I 3: I Experimental data has been read CONTINUE RETURN ITYPE I 1: Evaluate algebraic equation and residual CONTINUE IF(U(1).GT.0.)GO TO 1002 U(1)'1.E+09 CONTINUE IF(U(5).LT.1.)GO TO 1001 U(5)I.0001 CONTINUE IF(U(5).GT.0.)GO TO 1000 0(5)3 .0001 CONTINUE PII2’3.16159 ALPHAIT.ICONST(Z)*CMPLX(0.,1.)‘(CONST(3)°XX(1)‘PI+U(6)) ALPHBI1.ICONST(5)*CMPLX(0.,1.)*(CONST(6)'XX(1)‘PI+U(6)) BRUCE"(ALPHA*ALPHB+1./U(5)) FRED-(ALPHA-ALPHBICONST(6)/U(5)'CONST(1)/U(5))**2 BOOI6‘CONST(1)‘CONST(6)/(U(5)*U(5)) ALEXIFRED+808 ALICDEXP(CDLOG(ALEX)/2.) XLAMA8(BRUCE+AL)/2. XLAM8'(BRUCE-AL)/2. CIICMPLX(0.,1.)‘(XLAMB+CONST(1)‘ALPHA+CONST(6)‘ALPHB)/('XLAMA+ 1XLAMO) C2ICMPLX(0.,1.)‘(XLAMA+CONST(1)*ALPHA+CONST(6)‘ALPHB)/(XLAMA° 1XLAMB) XSI-C1*(CDEXP((XLAMA-CONST(8))‘CONST(7)))/(XLAMA-CONST(8))* 1('C2)'(CDEXP((XLAMB-CONST(8))‘CONST(7)))/(XLAMB-CONST(8)) 35 227 REAPIREAL(XS) AMAGIDIMAG(XS) CALCIU(1)‘('REAP‘SIN(U(3)'(CONST(3)'XX(1)‘PI+U(6))*CONST(7))+ 1AMAG‘COS(U(3)'(CONST(3)'XX(1)‘PI+U(6))‘CONST(7)))+U(2) IF (IMETH .NE. '1) GOTO 35 Simulations only RETURN Fits CONTINUE RESIDICALC°XX(2) RETURN ITYPE I 2: Set the initial conditions for differential eqn's CONTINUE Y(1) I 1.0E-20 NIEON I 1 I Set the WP of equations RETURN ITYPE I 3: Evaluate the differential eqn's CONTINUE IF (U(1) .LE. 0.0) U(1) I ABS(U(1)) IF (U(Z) .LE. 0.0) U(Z) I ABS(U(2)) CONC1 I CONST(1) CONCZ I CONST(2) DY(1) I U(1) * (CONC1 - Y(1))*(CONC2-Y(1))'(U(2)*Y(1)) RETURN c ..... C 5 20 10 228 ITYPE I 6: Calculate the residual for differential eqn's CONTINUE IF (IMETH .NE. -1) GOTO 20 Simulations only RETURN Fits CONTINUE CONST(6) is the molar absorptivity -- substitute exp val if known. CONST(6) I 5000.0 RESID I Y(1)+DLOG10(XX(2)/CONST(6))/(CONST(6)*0.2) RETURN ITYPE I 8: Calculate X(KVAR,I) the IPLT = 2 plotting mode ITYPE I 9: FOP(I) I X(KVAR+1,I) for the IPLT I 3 mode ITYPE I 10: FOP(I) = X(KVAR+2,I) for the IPLT = 6 mode 229 c .............................. C 11 COITINUE RETURN C C .............................. C C ITYPE I 11: FU(I) <<<< x-axis; F0(I) <<<< yaxis (IPLT = 5) C C .............................. C 12 CNTINUE RETURN C c .............................. C C ITYPE I 12: Called after sinulation C C .............................. C 13 CGITINUE RETURN END This is the subroutine of the equation for a two-site exchange NMR signals. To initialize the curve fitting process for this data file, which is a digitized format Of an NMR signal of the nuclei under a chemical exchange between the two sites, type on the VAX system: KINRUN NMRZSITEB TESTK(Or a file name in general). 230 Appendix I SUBROUTINE EQN-NHRISITE.FOR SUBROUTINE EON ("I n O O n O n O O O O O O n O n n n O O D n n n LORENTZIAN LINESHAPE CORRECTED FOR LINE BROADENING, DELAY TIME AND ZERO-ORDER DEPHASING. PARAMETERS U(1) II R (INTENSITY . UNITLESS) U(2) I T2 (RELAXATION TIME. SEC./RAD.) U(3) NU (FREOENCY. HERTZ.) U(6) THETA (ZERO ORDER PHASE CORRECTION. RAD.) 0(5) (BASELINE INTENSITY.UNITLESS.) CONSTANTS CONST(1) = DE (DELAY TIME. SEC.) CONST(Z) L8 (LINE BROADENING. HERTZ.) n IMPLICIT REAL*8(A-H,0-Z) IMPLICIT INTEGER*6(I-N) INCLUDE 'KINFIT:KINFITCOM.FOR/LIST' INCLUDE 'KINFIT:KINEONCOM.FOR/LIST' COMPLEX‘16 ALPHA,ALPHB,XLAMA,XLAMB,C1,C2,XS,8RUCE,ALEX,AL,FRED C ..................................................................... Entrleontrol Point C C ..................................................................... C GOTO (2,3,6,5,1,7,8,9,10,11,12,13) ITYPE C C .............................. C C ITYPE = 5: Initial call. No input has taken place C C .............................. C 1 CONTINUE HRITE (LUNOUT,8500) I Log the ID of this routine 8500 FORMAT (' '**EON: CEM 671 Method 2 (06-SEP-85)**") RETURN C C .............................. C C ITYPE I 6: Control card #1 and CONST have been input C c .............................. C 7 CONTINUE NMKIS NOVARIZ RETURN C C .............................. C C ITYPE I 3: I Experimental data has been read C C .............................. C 8 CONTINUE RETURN C C .............................. C C ITYPE I 1: Evaluate algebraic equation and residual c--- C c--- C 3 232 CONTINUE BROADI3.16159‘U(2)*CONST(2)+1 PHASEIZ.*3.16159*CONST(1)‘(XX(1)-0(3))+0(6) T0PIEXP(°CONST(1)*BROAD/U(2))*(COS(PHASE)'2.'3.16159*(U(2)/BR0AD)* 1(XX(1)'0(3))*SIN(PHASE)) BOTII.+(U(2)/BROAD)**2*(2.*3.16159*(XX(1)'U(3)))**2 CALCI0(1)‘(0(2)/BROAD)*T0P/BOT+0(5) IF (IMETH .NE. -1) GOTD 35 Simulations only RETURN Fits CONTINUE RESIDICALC-XX(2) RETURN ITYPE = 2: Set the initial conditions for differential eqn's CONTINUE YII) I 1.0E-20 NOEON I 1 I Set the number of equations RETURN ITYPE I 3: Evaluate the differential eqn's CONTINUE IF (0(1) .LE. 0.0) U(1) = ABS(U(1)) IF (0(2) .LE. 0.0) 0(2) I ABS(0(2)) CONC1 I CONST(1) CONC2 I CONST(Z) DY(1) I U(1) ' (CONC1 - Y(1))*(CONC2-Y(1))'(0(2)*Y(1)) 20 10 233 RETURN ITYPE I 6: Calculate the residual for differential eqn's CONTINUE IF (IMETH .NE. :1) GOTO 20 Simulations only RETURN Fits CONTINUE CONST(6) is the molar absorptivity -- substitute exp val if known. CONST(6) I 5000.0 RESID I Y(1)+DLOGID(XX(2)ICONST(6))/(CONST(6)*0.2) RETURN ITYPE I 8: Calculate XIKVAR,I) the IPLT = 2 plotting mode ITYPE I 9: FOP(I) I X(KVAR+1,I) for the IPLT I 3 mode 234 C C ITYPE I 10: FOP(I) I XIKVAR+2,I) for the IPLT I 6 mode C c .............................. C 11 CONTINUE RETRN C C .............................. C C ITYPE I 11: FU(I) <<<< x-axis; FO(I) <<<< yaxis (IPLT I 5) C C .............................. C 12 CONTINUE RETURN C .............................. C ITYPE I 12: Called after simulation C C .............................. C 13 CONTINUE RETURN END This is a subroutine KINFIT program for the fitting of the NMR signals not undergoing the exchange reactions. Relaxation times(T2 ) and frequencies(v) can also be Obtained by running this program, in alternative to the method by running the built-programs on Bruker-180 spectrometer. Here, the same procedures as running NMRZSITEB are performed in order to Obtain T2 and v. 10. 11. 12. 13. 14. 235 REFERENCES Pedersen, C.J. J. Am. Chem. Soc., 1967, 82, 7017 Pedersen, C.J. Fed.Proc., Fed. Am. Soc. Exp. Biol., 1968, g1, 1305 Pedersen, C.J. J. Am. Chem. Soc., 1970, 2, 386 Iehn, JQM. Structure Bonding, 1973, 1g, 1 Dietrich, 8.: Lehn, J.M. and Sauvage, J.P. Tetrahedron Lett., 1972, 2885-2889 Burgermeister, W. and Winkler-Oswatitsch, R. 292; Curr. Chem., 1977, g2, 91 Chock, P.B.: Eggers, F.: Eigen, M. and Winkler, R. Biophys. Chem., 1977, g, 239 Frensdorff, H.K. J. Am. Chem. Soc., 1971, 2;, 600 Christensen, J.J.: Eatough, D.J. and Izatt, R.M. Chem. Rev., 1974, 15, 351 Lardy, H. Fed. Proc., Fed. Am. Soc. Exp. Biol., 1968, 21, 1278 Eiseman, G.: Ciani, S.M. and Szabo, G. Fed. Proc., Fed. Am. Soc. Exp. Biol., 1968, 21, 1289 Tostesen, D.C. Fed. Proc., Fed. Am. Soc. Exp. Biol., 1968, 21, 1269 Eiseman, G. Fed. Proc.. Fed. Am. Soc. Exp. Biol., 1968, 31, 1249 Pressman, D.C. Fed. Proc., Fed. Am. Soc. Exp. Biol., 1968, g1, 1283 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 236 Izatt, R.M.: Rytting, J.H.: Nelson, D.C.: Haymore, B.L. and Christensen, J. Science, 1968, 63, 444 Chem. Eng. News, 1970, 38(2), 26 Kolthoff, I.M. Anal. Chem., 1979, gglgl, 1R Liesegang, G.W. and Eyring, E.M. in "Synthetic Multidentate Macrocyclic Compounds", edited by Reed, R.M. and Christensen, J.J. Academic Press, New York, 1978, pp245-287 Eigen, M.: Winkler, R. in "The Neurosciences, 2nd Study Program". Schmitt, F.0., Ed. Rockefeller University Press, New York, N.Y., 1970, p 685 Liesegang, G.W.: Farrow, M.M.: Purdie, N. and Eyring, E.M. J. Am. Chem. Soc., 1976, fl, 6905-6909 Chock, P.B. Proc. Natl. Acad. Sci. U.S.A., 1972, 62, 1939 Petrucci, S.: Adamic, R.J. and Eyring, E.M. J. Chem. Phys., 1986, 2g, 1677-1683 Maynard, R.J.: Irish, D.E.: Eyring, E.M. and Petrucci, S. J. Chem. Phys., 1984, 88, 729-736 Rodriguez, L.J.: Liesegang, G.W.: White, R.D.: Farrow, M.M.: Purdie, N. and Eyring, E.M. J. Chem. Phys., 1977, 81, 2118-2122 Chen, C.C.: Petrucci, S. J. Chem. Phys., 1982, 88, 2601-2605 Wallace, W.: Chen, C.: Eyring, E.M. and Petrucci, S. J. Chem. Phys., 1985, 82, 1357-1366 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 237 Lehn, J.M., and coworkers, J. Am. Chem. Soc., 1970, 2;, 2916 Loyola, V.M.: Wilkins, R. and Pizer R. J. Am. Chem. £994, 1975, 91, 7382 Henco, K.: Tfimmler, B. and Maass, G. Angew. Chem., Int. Ed. Engl. 1977, 16, 538 Cox, B.G. and Schneider, H. J. Am. Chem. Soc., 1977, 22, 2809 Gresser, R.: Albrecht-Gary, A.M.: Lagrange, P. and Schwing, J.P. Nouv. J. Chim., 1978, 1, 239 Cox, B.G.: Schneider, H.: Stroka, J. J. Am. Chem. §£L 1978, 1%, 4746-4749 Cox, B.G.: Schneider, H. Inorganic Chimica Acta, 1982, 61, L263-L265 Cox, B.G.: Garcia-Rosas, J. Ber. Bunsenges Phys. Chem., 1982, 86, 293-297 Kodama, 11.: Kimura, E. J.C.S.Chem.Comm., 1975, 326 Kodama, M.: Kimura, E. J.C.S. Dalton, 1976, 116-119 Kodama, M.: Kimura, E. J.C.S. Dalton, 1977, 2269-2276 Hinz, F.P and Margerum, D.W. J. Am. Chem. Soc., 1974, 26, 4993; Inorg. Chem. 1974, 12, 2941 Busch, D.II.: Farmery, K.: Goedken, V.: Katovic, V.F Melnyk, A.C.: Sperati, C.R. and Tokel, N. Adv. Chem. &, 1971, No.100, 44 Degani, H. Biophys. Chem, 1977, 6, 345-349 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 238 Funck, F.: Eggers, F. and Grell, E. Chimica, 1972, ;§, 637 Liesegang, G.W.: Farrow, M.M.: Vazquez, F.A.: Purdie, N. and Eyring, E.M. J. Am. Chem. Soc., 1977, 3240 Dibler, H.: Eigen, M.: Ilgenfrita, G.: Maass, G.: Winkler, R. Pure Appl. Chem., 1969, 22, 93 Cox, B.G.: van Trugon, NG: Rzeszotarska, J.: Schneider, H. J. Am. Chem. Soc., 1984, 126, 5965 Pointud, Y.: Tissier, C.: Juillard, J. J. Solution Chem., 1983, l, 473 Hoogerheide, J.G.: Popov, A.I. J. Solution Chem., 1979, g, 83 Eyring, E.M.: et al. J. Phys. Chem., 1986, IND 0 6571-6576 Eyring, E.M.: et al. J. Phys. Chem., 1986, 29, 1659-1663 Cox, B.G.: Truong, N.V.: Garcia-Rosas, J.: Schneider, H. J. Phys. Chem. 1984, 88, 996-1001 Strasser, 8.0.: Shamsipur, M.: Popov, A.I. J. Phys. Chem., 1985, 82, 4822 Shchori, E.: Jagur-Grodzinski, J.: Luz, Z. and Shporer, M. J. Am. Chem. Soc., 1971, 2;, 7133 Lin, J.D., and Popov, A.I. J. Am. Chem. Soc., 1981, 19;, 3773 Strasser, 8.0.: Hallenga, K.: Popov, A.I. J. Am. Chem. Soc., 1985, 1 7, 789-792 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 239 Carvajal, C.: TOlle, R.J.: Smid, J.: Szwarc, M. E; An. Chem. Soc. 1965, 81, 5548 Smid, J.: Grotens, A.M. J. Phys. Chem., 1973, 11, 2377 Bhattacharyya, D.N.: Lee, C.L.: Smid, J.: Szwarc, M. J. Phys. Chem., 1965, 52: 612 Gutmann, V. "Coordination Chemistry in Nonaqueous Solutions", New York, Springer-Verley (1968) Cox, B.G.: Garcia-Rosas, J. and Schneider, H. J. Am. Chem. Soc., 1981, ;_;, 1054-1059 Mei, E.: Popov, A.I. J. Phys. Chem., 1977, 8;, 1677 Cox, B.G.: Guminsky, C.: Firman, P. and Schneider, H. J. Phys. Chem., 1983, 81, 1357-1361 Chen, C.: Wallace, W.: Eyring, E. and Petrucci, S. 2; Phys. Chem., 1984, 88, 2541-2547 Grell, E. and Oberbéumer, in "Chemical Relaxation in Molecular Biology", Pecht, I.: Rigler, R. ED., Springer-Verlag, Berlin, 1977 Cox, B.G.: Truong, N.G. and Schneider, H. J. Am. Chem. Soc., 1984, 129: 1273-1280 Shamsipur, M.: Popov, A.I. J. Phys. Chem., 1988, 88, 147 Schmidt, E.: Popov, A.I. J. Am. Chem. Soc., 1983, 888, 1873-1878 Cahen, Y.M.: Dye, J.L.: Popov, A.L. J. Phys. Chem., 1975, 18, 1292-1295 67. 68. 69. 700 71. 72. 73. 74. 75. 76. 77. 78. 79. 240 Shamsipur, M.: Popov, A.I. J. Phys. Chem., 1987, 8;, 447-451 Ceraso, J.M.: Smith, P.B.: Landers, J.S.: Dye, J.L. J. Rhys. Chem., 1977, 8;, 760-766 Shchori, E.: Jagur-Grodzinski, J.: Shporer, M. J. Am. Chem. Soc., 1973, 88, 3842 Laidler, R.J. "Chemical Kinetics", McGraw-Hill: New York, 1965, p251 Schmidt, E. Ph.D. Thesis, 1981, Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 Strasser, B. Ph.D. Thesis, 1984, Department of Chemistry, Michigan State University, East Lansing, Michigan 48824: a.p81 and p160. Szczygiel, P.F. Master Degree Thesis, 1984, Department of Chemistry, Michigan State University, East Lansing, Michigan 48824: a. p.52: b.8: c.54 Sirlin, C. Bull. Soc. Chim. Fr., 1984, II-S Szczygiel, P.: Shamsipur, M.: Hallenga, K.: Popov, A.I. J. Phys. Chem., 1987, 8;, 1252-1255 Delville, A.: Stover, H.D.: Detellier, C. J. Am. Chem. Soc., 1985, 881, 4172 Buschmann, R.J. Inorg. Chim. Acta., 1985, 88, 43 Okoroafor, N.: Popov, A.I. in press Riddick, J.A.: Bunger, W.B. "Techniques of Chemistry- Volume II: Organic Solvents", 3rd Edition, 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 241 Weissberger, A. ed., Wiley-Interscience, New York, (1970), p.353 Okoroafor, N.O. Ph.D Thesis, 1987, Department Of Chemistry, Michigan State University, East Lansing, Michigan 48824 Shaw, D. "Fourier Transform NMR Spectroscopy", second edition, IGE Medical Systems Ltd., Slough, Berkshire, United Kindom Abragam, A. "The Principles of Nuclear Magnetism", Oxford University Press, LondOn, 1961 Deverell, C. Prog. Nucl. Magn. Reson. Spectrosc., 1969, g, 278 Lincoln, S.F. Progress in Reaction Kinetics, 1977, vol.9, No.1., pp. 1-91 Gupta, R.K.: Pitna, T.P.: Wasylishen, R. J. Magn. 822;: 1974, 8;, 383 Live, D.H.: Chan, S.I. Anal. Chem., Vol. 42, No. 7, 791 Van Geet,A.L. Anal. Chem., 1968, 88, 227 Van Geet,A.L. Anal. Chem., 1970, Kaplan, M.L.: Bobey, F.A.: Chang, H.N. Anal. Chem., 1975, 31, 1703 Nicely, V.A.: Dye, J.L. J. Chem. Educ., 1971, 88, 443 Petrucci and coworkers, personal communications. 92. 93. 94. 95. 96. 97. 98. 99. 100. 242 Lin, J.D. Ph.D Thesis, 1980, Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 Burkhard Tuemmler: Gueter Maass: Fritz Vogtle: Heenz Sieger: Ulrich Meimann: Edwin Weber a. J..Am. Chem. §222 1977, 88, 4683 - 4690: J. Am. Chem. Soc., 1979, 121: 2588 - 2598 Erlich, R.H.: Popov, A.I. J. Am. Chem. Soc., 1971, 88, 5620 Burden, I.J.: Coxon, A.C.: Stoddart, J.P.: Wheatley, C.M. J. Chem. Soc., Perkin Trans. I, 1977, 220-226 Takeda, Y. Bull. Chem. Soc. Jpn., 1983, 88, 866-868 Kolthoff, I.M.: Chantooni, M.K.: J. Anal. Chem., 1980,88, 1039-1044 Smetana, A.J.: Popov, A.I. J. Solution Chem., 1980, 8, 183-196 Perelygin, I.S. et al., 8. Russ. J. Phys. Chem. 1986, 88, 1474: b. Russ. J. Phys. Chem. 1973, 81, 1138, Mosier-Boss, P.A. Ph.D Thesis, 1985, Department Of Chemistry, Michigan State University, East Lansing, Michigan 48824