Investigation of Crown Ether Cation

Investigation of crown ether cation-

systems using electrophoretic NMR

Fredrik Petersson physical Chemistry royal institute of technology (KTH) Stockholm Sweden

Supervisor Marianne Giesecke

Examiner prof Istvan´ Furo´

Stockholm June 29, 2012 Abstract

The purpose of this thesis was to investigate how crown ethers behave and interact with different cations and to optimise the setup of the electrophoretic NMR. To get a good electrophoretic NMR measurement the electrophoretic phase shift needs to be big. To increase the phase shift some parameters needed to be adjusted, parameters such as the concentration of crown ether and cation, the duration of magnetic field gradient pulse δ, the magnetic field gradient strength g,the diffusion time Δ and the applied voltage V. The main focus then put on crown ethers 15-crown-5 and 18-crown-6. The cations used were lithium (Li), sodium (Na), potassium (K), caesium (Cs), calcium (Ca) and barium(Ba). The effective charge was obtained by using pulsed gradient NMR to derive the diffusion coefficient and electrophoretic NMR to get the electrophoretic mobility. These data were used to calculate the equilibrium constant of the formed complex. The outcome of the investigation: the affinity for 18-crown-6 was in the following order

barium > potassium > caesium > sodium > calcium > lithium

and for 15-crown-5

barium > sodium > calcium > caesium > potassium > lithium.

Sammanfattning

Syftet med denna avhandling var att undersöka hur kronetrar beter sig och inter- agerar med olika katjoner och optimera den elektroforetiska NMR uppsättningen, För att f˚a en bra elektroforetiska NMR mätning m˚aste fasskiftet vara stort. För attoka ¨ fasskiftet behövs n˚agra parametrar ställas in s˚a som koncentration av kroneter och katjon, längden av magnetfältsgradientspulsen δ, den gradi- entstyrkan g, diffusionstiden Δ och den applicerade spänningen V. Fokus har lagts p˚a kronetrarna 15-kron-5 och 18-krona-6. De använda katjoner var litium (Li), natrium (Na), kalium (K), cesium (Cs), kalcium (Ca) och barium (Ba). De olika systemen undersöktes med hjälp av diffusions NMR för att mäta diffu- sionskoefficienten och elektroforetisk NMR för att f˚a fram elektroforetiska mo- biliteten. Dessa uppmätta data användes för att beräkna jämviktskonstanten av det bil- dade komplexet. Utfallet av studien blev: affiniteten för för 18-kron-6

barium > kalium > cesium > natrium > kalcium > litium

i och f¨or 15-kron-5

barium > natrium > kalcium > cesium > kalium > litium.

ii Contents

Abstract...... i Sammanfattning...... i Contents...... iii Introduction...... iv

1 Background 1 1.1Crownethers...... 1 1.2Acetatesalts...... 2 1.3Electrophoresis...... 2 1.4DiﬀerenttypesofNMRtechniques...... 3 1.4.1 ConventionalNMR...... 3 1.4.2 PulsedﬁeldgradientNMR...... 6 1.4.3 ElectrophoreticNMR...... 10

2 Summary of research 14 2.1Assemblingoftheelectrophoreticcell...... 14 2.2Calibration...... 14 2.2.1 Calibrationoftheelectrophoreticcell...... 14 2.2.2 Calibration of the diﬀusion measurement ...... 15 2.2.3 Calibrationofthegradient...... 16 2.3Samplepreparation...... 16

3 Results and discussion 19 3.1Diﬀusionmeasurements...... 19 3.2ElectrophoreticNMR...... 19 3.3Summaryofresults...... 23 3.4Sourcesoferrors...... 24

4 Conclusions 25

Acknowledgements 26

Bibliography 28

Appendix 29

List of ﬁgures 43

iii Introduction

Crown ethers interaction with cations are fairly well known, but not so many studies have been using electrophoretic NMR. Crown ethers are of interest because their properties are useful in applications such as catalysts for chemical reactions [1], phase transfer reagents, increasing solubility of salts in organic liquids [19], hosts for transport across membranes [3] and separation processes [25]. To investigate the interaction between crown ethers and cations, three different NMR techniques were used: conventional NMR, pulsed field gradient NMR and electrophoretic NMR. Conventional NMR uses the magnetic moment of nuclei, to derive information about their surroundings. In pulsed gradient NMR magnetic field gradients are applied to achieve a loss in signal strength of the peaks in the spectra. The behaviour of the decaying signal can be used to derive the diffusion coefficient Electrophoretic NMR is a combination between electrophoresis and pulsed gradient NMR and measures phase shift in the spectra under increasing electric field and constant magnetic field gradient. If the diffusion coefficient is known then the technique makes it possible to derive information like: electrophoretic mobility, effective charge and equilibrium constant.

iv Chapter 1

Background

1.1 Crown ethers

The first crown ether was synthesized in 1967 by Charles J Pedersen [18]. This discovery later gave him the Nobel prize in 1987 together with Jean-Marie Lehn and Donald J Cram for their development and use of molecules with structure- specific interactions of high selectivity.[24] Crown ethers are ethers with a closed structure. To optimise the molecular dipole moment the chain folds into something that reminds of a crown, hence the name. The closed structure gives rise to a cavity and this is the origin of its interesting properties, such as binding to different cations. These phenomena can exist thanks to the interaction between the oxygen atoms in the crown ether and the cation in the cavity, this lowers the free energy for the complex con- stituents. Properties that influence the free energy are the charge of the cation, rigidity of the crown ether, entropic effects, solvation shells surrounding the complex and cation, size of the cation and the crown ether. The size selectivity tends to decrease as the ring size of the crown ether increases, since it is easier for a larger ether to achieve a folded configuration to optimise its interaction with the cation, because of the high flexibility.[24, 11] The sum of the thermodynamic effects gets reflected in the equilibrium constant

[crown ether cation complex] K = . (1.1) [freecation][unoccupied crown ether]

The equilibrium constant varies with the cation, which makes it possible to separate cations from each other by using a crown ether that is selective to one of the cations in the system [25]. Other applications for crown ethers are catalysts for chemical reactions [1], phase transfer reagents, they can also increase the solubility of salts in organic liquids [19] The crown ethers used in this thesis are 15-crown-5 and 18-crown-6 with cavity sizes of approximately 1.3-1.7 A˚ respectively 0.9-1.1 A,˚ see Figure 1.1.

1 O O

O O O O

O O O O O

(a) (b) 15crown5 18crown6

Figure 1.1: Crown ethers used in this thesis.

1.2 Acetate salts

The advantage with acetate salts is that the acetate anion has protons and can be easily detected by 1H NMR. The cations to acetate explored here are listed in Table 1.1 together with their respective ionic radius [16]

Cation Ionic radius [A]˚ Li+ 0.69 Na+ 1.02 K+ 1.38 Cs+ 1.70 Ca2+ 1.00 Ba2+ 1.36

Table 1.1: Cations used in this work [16]

1.3 Electrophoresis

In electrophoresis the behaviour of charged spices in field is used. According to fundamental physics a charged particle in an electric field is influenced by a force [9] qU Fe = , (1.2) l where Fe is the force in [N], q is charge of the particle in [C], U is the electric potential difference in [V] and l is the distance between the electrodes in [m]. This phenomenon is explored in electrophoresis. If the particle is not moving in vacuum, its movement interferes with the surrounding medium which corresponds to a friction force that is acting to restrict motion. The friction force is dependent of the speed and the interaction between the particle and the medium and is given by the equation: Ff = fv (1.3)

2 −1 where Ff is the friction force in [N], f the friction coefficient in [Nsm ]andv the velocity in [ms−1]. When the two forces are equal then the acceleration stops and the particle travels at a constant speed which gives the following expression. qU v = (1.4) lf The self motion of a system in a medium is called diffusion and it depends on the thermal energy of the systems and the resistance against movement. The diffusion is described by the Einstein-Sutherland equation:

kB T D = , (1.5) f

2 −1 where D is the diﬀusion coeﬃcent in [m s ], kB is the Boltzmann factor in [JK−1]andT is the temperature in [K]. By combining eq 1.4 and eq 1.5 the following expression can be derived.

vkB Tl D = (1.6) qU The definition of electrophoretic mobility is vl μ = (1.7) U which makes it possible to express the diffusion coefficient in the following way [7] μkB T D = . (1.8) q

1.4 Diﬀerent types of NMR techniques

Different types of modified setups of Nuclear Magnetic Resonance spectroscopy (NMR) have been proven to be powerful for deriving information about structure, diffusion properties and electrophoretic mobility for different NMR active substances. [21, 7, 10]

1.4.1 Conventional NMR NMR exploit the nuclear spin properties of different atoms, which is useful to determine the local environment surrounding every NMR active nuclei. In order not to violate basic quantum mechanic, the spin of the nuclei, denoted by I, has to be quantized, as described by the magnetic quantum number mI .Ina magnetic field the different magnetic quantum numbers correspond to different energies [10] mI γhB E = (1.9) 2π where E is energy in [J], B the magnetic field strengthen at the site of the active nuclei in [Tesla(T )], γ is the gyromagnetic ratio [s−1T −1]andh is Planck constant [Js].

3 Figure 1.2: The 90o pulse and the subsequent FID [7]

Because of the energy difference the system gets a net magnetisation in the orientation of the static magnetic field (called thermal equilibrium). Transitions between states with different magnetic quantum number ΔmI =1 give by equation[10] γhB ΔE = . (1.10) 2π Because of the relation ΔE = hω (1.11) where ω is a frequency in [Hz], combining 1.10 and 1.11, yields the so called Larmor frequency [10] γB ω = (1.12) 2π which sets the conditions for resonance excitation. To analyse the sample it has to be manipulated out of thermal equilibrium, which can be achieved by applying a radio frequency pulse at the Larmor frequency. This induces a torque on the net magnetization and it turns it away from its equilibrium. The resulting orientation of the net magnetization relative to the static field depends of the intensity of the applied radio frequency pulse and its duration. Most common is to use pulses that turn the net magnetization 90o and 180o. The maximum detectable signal occurs after a 90o pulse, see fig 1.2, because then all the magnetisation is in the xy plane where it is possible to detect. [22] Nucleiofthesametypeofisotopeinthesamespectrometercanhavedifferent Larmor frequency, because eq 1.12 is dependent on magnetic field. And there is a slight difference, depending on their close environment and especially the density of electrons surrounding the nuclei, a high density of electrons has a tendency to shield the magnetic field, so the sensed magnetic field will be less than the applied, and this makes it possible to separate signals from different molecules. Of the same reason, it is possible to collect information about the nuclei surroundings. These days NMR is a pulsed method, instead of scanning through all radio fre- quencies one at a time (as had to be done before the 1970s). This approach saves a lot of time which makes it possible to get a better signal to noise ratio in loss of time.[4]

4 Figure 1.3: 1D 1H NMR spectrum of 10 mM 18-crown-6 and 10 mM barium acetate dissolved in D2O, the peeks in the spectra, starting from the left correspond to water, crown ether and acetate

To get the FID (free induction decay), see 1.2, the voltage that is introduced by the time dependent magnetisation in the xy-plane needs to be plotted against time. Transformation from time domain to frequency domain (so called Fourier transform) creates a one-dimensional chemical shift dependent spectrum, see fig 1.3. [2] Two properties that are important to consider when measuring are the longitudinal (T1) and transverse (T2) relaxation. Longitudinal relaxation time is a measure of how fast the system reaches thermal equilibrium after having been excited. The process is typically described as [5] t Δn(t)=Δneq 1 − exp − (1.13) T1 where Δn(t) is the population difference between energy levels after the time t, Δneq is the population difference at equilibrium and T1 the longitudinal relaxation time in [s]. The pulse program inversion recovery (see fig 1.4) can be used for measuring T1. Transverse relaxation time is a measure how fast the magnetic component perpendicular to the static field is lost.Both relaxation times are influenced by molecular dynamics in the chemical system. [15] The reason for relaxation is fluctuations in the magnetic field.[10] Mechanisms that give short relaxation times are quadrupolar and paramagnetic relaxation. 1 Quadrupolar relaxation occurs only for nuclear spins higher then 2 . Paramag- 1 netic relaxation occurs when a nucleus with spin 2 interacts with a paramagnetic

5 Figure 1.4: Inversion recovery species (element or molecule with an unpaired electron). [2, 15, 14]

1.4.2 Pulsed field gradient NMR Pulsed field gradient NMR is a modification of conventional NMR. Instead of keeping B0 field constant it is made dependent on the position along the z-axis dBz (same direction as the B0 magnetic field) dz =0. Two commonly used pulse programs are the spin-echo and stimulated echo, see fig 1.5 and fig 1.6. A difference between the two pulse programs is in which direction the magnetisation is stored under the principal duration of the pulse program, so the choice of pulse program depends on the T1 and T2 relaxation of the investigated sample. Stimulated echo tends to give less artefacts in the measurement and therefore it is the most commonly used. There also exists a double stimulated echo which is a combination of two stimulated-echo pulse programs after each other. The Larmor frequency of the nucleus see, eq 1.12, is dependent on the magnetic field. By applying a magnetic field gradient the Larmor frequency of the nucleus becomes dependent on position along the gradient. This can be used to follow compounds that move randomly (called self diffusion) in between the two gradient pulses. The change in environment corresponds to an offset of the Lar- mor frequency. The magnitude of the offset is dependent on the gyromagnetic ratio, the gradient field strength, the duration of the magnetic field pulse and the difference at the times of the two magnetic field gradient pulses according to equation 1.14 φ = γδg(z1 − z0). (1.14) A random offset leads to the decay of the signal.[21, 22, 13, 7] If the diffusion is isotropic (which it is if the components are not limited to a confined space in any direction) the Stejskal-Tanner equation is valid S δ = exp −γ2δ2g2D Δ − (1.15) S0 3

where S is the signal intensity with magnetic ﬁeld gradient applied, S0 is the signal intensity without magnetic ﬁeld gradient applied, γ is the gyromagnetic

6 Figure 1.5: The spin-echo pulse sequence

Figure 1.6: The stimulated echo pulse sequence

7 Figure 1.7: Diﬀusion plot obtained in a system consisting of 10 mM 18-crown-6 and 10 mM barium acetate dissolved in D2O. The peaks corresponds to, from the left, water, crown ether and acetate

ratio in [s−1T −1], δ is the duration of magnetic field gradient pulse in [s], g is the magnetic field gradient strength [Tm−1], D is the diffusion coefficient in [m2s−1] and Δ is the diffusion time in [s]. By plotting the signal intensity against the magnetic field strength, as the rest of the variables are constant, the diffusion coefficient can be calculated according to equation 1.15. For more detailed information see ref [21]. In fig 1.8 the signal intensity is plotted as a function of the magnetic field gradient If the two relaxation times are short (a few milliseconds), then it can be hard to measure the diffusion because the decay of the signal occurs fast even without any magnetic field gradient applied.

8 Figure 1.8: Diﬀusion plot of 18-crown-6 in a system consisting of 10 mM 18- crown-6 and 10 mM barium acetate dissolved in D2O

Figure 1.9: The double stimulated echo pulse sequence [7]

9 1.4.3 Electrophoretic NMR Electrophoretic NMR is a method that combines electrophoresis with diffusion NMR. For being able to achieve the fusion of the two techniques the NMR cell needs to be modified. Hence two electrodes had been added into a 5 mm NMR tube, see fig 1.12. The modification made it possible to apply a potential difference over the sample length. The generated electric field, is responsible for a movement of all charged particles present in the sample. The resulting plug- flow along the z-axis will be responsible for a phase shift in the spectrum. The experiment is usually set up in that manner that positive species gives positive phase shift and negative specie give a negative phase shift, but this is just a matter of convention. Because of the applied electric field, the pulse program used in diffusion NMR also needs to be modified. In fig 1.11, a pulse program of an electrophoretic double stimulated echo is shown. It is quite similar to an ordinary double stimulated echo mentioned in the pulsed gradient NMR part, fig 1.9. Here two electrophoretic pulses are included, the direction of the electric field is switched Δ to the opposite after half the diffusion time 2 . The pulse program has the advantage to suppresses phase shifts as an artefact of thermal convection. This is possible because thermal convection is independent on the electric field. For a more detailed explanation, see [7] and [12] There are additional effects that influence the bulk flow (and the electrophoretic double stimulated echo cannot suppress all convection effects). This makes it important to keep track on the movement of uncharged species, because these species can be used as a reference of how the bulk is flowing. By subtracting the phase shift of the charged compounds from that of the uncharged, once the tuned electrophoretic phase shift can be derived. In this thesis water was used as reference.[7] If the phase shift is plotted as a function of applied voltage, (see fig 1.10), the slope can be used to derive the electrophoretic mobility, according to the following equation l φ μ = (1.16) γgδΔ U where μ is electrophoretic mobility in [m2V −1s−1], l is the distance between the two electrodes in [m], γ is the gyromagnetic ratio in [s−1T −1], g is the magnetic field gradient in [Tm−1],δ diffusion time in [s], Δ is the duration of the gradient pulse in [s], φ is the phase shift in [rad]andU the applied voltage in [V ]. When the electrophoretic mobility is known, it is possible to calculate the effective charges z μkB T z = (1.17) De −1 where kB Boltzmann constant in [JK ], T the temperature in [K] and e the elementary charge in [C].

10 Figure 1.10: Spectra recorded in an electrophoretic NMR experiment plotted against applied voltage, for a system consisting of 10 mM 18-crown-6, 10 mM barium acetate dissolved in D2O. The peaks correspond, from the left, water and crown ether. The peak of acetate is not included in the spectra.

11 Its possible to use the effective charge z and the starting concentration of crown ether to calculate the concentration of cation crown ether complexes at equilibrium looks like following z [crown ether cation complex]= [crown ether]. (1.18) n were n is the nominal charge of the cation, z the effective charge of the crown ether and [crown ether] is the starting concentration of crown ether in [mol l−1] The difference between the starting concentration of crown ether and the concentration of cation crown ether complexes at equilibrium gives the free crown ether concentration at equilibrium z [unoccupied crown ether]=[crown ether] − [crown ether]= n z =(1− )[crown ether] (1.19) n and similar for the free cation concentration at equilibrium z [freecation]=[Xn] − [crown ether] n were [X ] is the starting concentration of the cation in [mol l−1]. If the ratio is 1:1 between [Xn]and[crown ether] as it was in this thesis the free cation concentration at equilibrium can modified z z [freecation]=[Xn] − [Xn]=(1− )[Xn]. (1.20) n n By modifying eq 1.1 using eq 1.18-1.20 following expression for the equilibrium constant can be derived z n [crown ether] K = z 2 n . (1.21) (1 − n ) [crown ether][X ]

[7]

12 Figure 1.11: The electrophoretic double stimulated echo (EPGDSTE) pulse sequence [7]

Figure 1.12: The appearance of the electrophoretic NMR cell [7]

13 Chapter 2

Summary of research

2.1 Assembling of the electrophoretic cell

The electrodes of cell were constructed of palladium wire with 500 μm diameter, the distance between the electrodes was 34.2 mm. For more details, see ref [8], note that in our case no silicon was used to seal the end of the glass capillaries.

2.2 Calibration

During this project diﬀerent calibrations were performed to achieve accurate data.

2.2.1 Calibration of the electrophoretic cell To calculate the electrophoretic mobility, the distance between the two electrodes in the cell must be determined (see fig 1.12). This is done by measuring the phase shift at different applied voltages. For a sample with known electrophoretic mobility. A 10mM tetramethylammonium bromide (≥ 99.0 %, Merck) (N(CH3)4Br)solution in D2O (99.9 atom% D, Isotec inc) was used for this purpose. The measurement was performed three times and the solution was changed each run. The pulse program used was an electrophoretic double-stimulated echo developed py Pettersson et al [20], see fig 1.11, the duration of the magnetic field gradient δ was set to 1 ms, the diffusion time Δ to 200 ms, the gradient field strength g to 25 Gcm−1 and the potential difference was stepped up from 0 V up to 400 V in 10 equal steps. By using equation 1.16 and rearranging the parameters, the distance between the two electrodes was given by the relation: −1 φ l = μγgδΔ U The average length was obtained as. −1 −1 −1 μγgδΔ φ φ φ ¯l = + + 3 U 1 U 2 U 3

14 Figure 2.1: Experiments and data for calibration of electrode distance using 10 mM N(CH3)4Br in D2O

By using the known electrophoretic mobility and the average slope of the measurement, see ﬁg 2.1, the length could be calculated as. 180 3.749 ∗ 10−8 ∗ 26.75 ∗ 107 ∗ 53.5 ∗ 0.9 ∗ 0.52 ∗ 0.2 ∗ 10−3 l¯= × π 100 [0.8172]−1 +[0.8358]−1 +[0.8391]−1 × =0.0346 m 3 180 π is a conversion constant to transform degrees into radians. The standard deviation was calculated as

−1 −1 2 −1 −1 2 −1 −1 2 φ ¯φ φ ¯φ φ ¯φ U − U + U − U + U − U 1 2 3 ±s = μγgδΔ = 2 = ±0.000496 m The value 34.6 ± 0.5 mm was then used as the length between the electrodes in all the ﬂowing electrophoretic measurements.

2.2.2 Calibration of the diffusion measurement The diffusion calibration was made by performing three diffusion measurements, on a mixture consisting of HDO/D2O with known T1 relaxation time of 290

15 ms. The outcome from the measurement gave an average diffusion coefficient of 1.889 ∗ 10−9m2s−1 which was compared with published data for the same ∗ −9 2 −1 D0 system 1.902 10 m s [17]. The ratio between Dmeasured was 1.00688, every measured diffusion coefficient was multiplied with this value. [23]

2.2.3 Calibration of the gradient The gradient strengthen can be calibrated by using the measured diﬀusion co- eﬃcient and the tabulated value derived by Mills [17] and using equation Dapp g = gapp (2.1) D0

where g is the actual gradient strength, gapp is the gradient strength specified by the used probe, Dapp is the measured diffusion coefficient and D0 is the diffusion coefficient from the publication[17]. The gradient calibration constant was calculated to be 0.99658. [23]

2.3 Sample preparation

The following chemicals were used during the whole project lithium(I) acetate (99.95 %, Sigma Aldrich), sodium(I) acetate (≥ 99.0 %,Sigma Aldrich), potassium(I) acetate (≥ 99.0 %, Sigma Aldrich), caesium(I) acetate (99.9 %, Sigma Aldrich), calcium(II) acetate monohydrate (≥ 99.0 %, Sigma Aldrich), barium(II) acetate (≥ 99.0 %, Sigma Aldrich), gadolinium(III) chloride anhy- drous(99.99, Sigma Aldrich), cerium(III) sulphate hydrate(insoluble matter 0.10 %, GFS G.Frederick Smith chemical company), 18-crown-6 (≥98%, Alfa), 15- crown-5 (98%, Alfa), and deuterium oxide (99.9% D, Isotec inc). The total number of samples was 24, see table 2.1, the crown ether and cation concentration were the same in all samples and they were set to 10±0.5 mM. The purpose of the samples with 10 % H2O (sample 13-24) was to improve the precision of the phase shift determined in the electrophoretic measurement, where limiting factor was the weak water signal. Measurements involving tuning of concentration of all samples, diffusion and electrophoretic measurements of the samples 1-12, were performed on a Bruker Avance 500 MHz using a BB inverse probe with z-gradient and maximum magnetic field gradient 51.3 G.cm−1. The diffusion and electrophoretic measurements of the samples 13-24, were performed on a Bruker Avance III 500 MHz using a diff 30 z-gradient probe with maximum magnetic field gradient 1800 G.cm−1. The first step were to prepare four 10 mM solutions consisting of the two different crown ethers solved in the two solvents, the concentration was tuned by using the integral in a 1H NMR spectra the reference used consisted of an 100 mM tetramethylammonium bromide solution solved in D2O.(This procedure was necessary because of former experiment resulted in that the integral shown a different relation between the cation and the crown ether then the measured weight.) The concentration of the four crown ether solutions were tuned until the concentration corresponded to 10 mM. These four samples were then used for dissolving the following salts: lithium acetate, sodium acetate, potassium acetate, caesium acetate, calcium acetate

16 Samples Sample number Salt Crown ether Solvent 1 Li acetate 18-crown-6 D2O 2 Na acetate 18-crown-6 D2O 3 K acetate 18-crown-6 D2O 4 Cs acetate 18-crown-6 D2O 5 Ca acetate 18-crown-6 D2O 6 Ba acetate 18-crown-6 D2O 7 Li acetate 15-crown-5 D2O 8 Na acetate 15-crown-5 D2O 9 K acetate 15-crown-5 D2O 10 Cs acetate 15-crown-5 D2O 11 Ca acetate 15-crown-5 D2O 12 Ba acetate 15-crown-5 D2O 13 Li acetate 18-crown-6 10% H2O 90% D2O (v/v) 14 Na acetate 18-crown-6 10% H2O 90% D2O (v/v) 15 K acetate 18-crown-6 10% H2O 90% D2O (v/v) 16 Cs acetate 18-crown-6 10% H2O 90% D2O (v/v) 17 Ca acetate 18-crown-6 10% H2O 90% D2O (v/v) 18 Ba acetate 18-crown-6 10% H2O 90% D2O (v/v) 19 Li acetate 15-crown-5 10% H2O 90% D2O (v/v) 20 Na acetate 15-crown-5 10% H2O 90% D2O (v/v) 21 K acetate 15-crown-5 10% H2O 90% D2O (v/v) 22 Cs acetate 15-crown-5 10% H2O 90% D2O (v/v) 23 Ca acetate 15-crown-5 10% H2O 90% D2O (v/v) 24 Ba acetate 15-crown-5 10% H2O 90% D2O (v/v)

Table 2.1: Samples prepared

and barium acetate. Resulting in the 24 samples shown in tab 2.1. The salt concentration of the solutions were tuned by 1H NMR spectra until a deviation from an 1:1 molar relation between the crown ether and the cation was less than 5 %. This procedure was necessary because of the calculated concentration based on the weighed mass of the salts were not accurate, due to the hygroscopic properties of the salts. Two T1 measurements were performed on the sample number 3 to derive T1 for 18-crown-6, acetate and sample number 7 to get T1 for 15-crown-5. The pulse was inversion recovery (see fig 1.4). The purpose of the two measurements were to optimise the parameters for the upcoming diffusion and electrophoretic measurement. The results gave a T1 for 18-crown-6 of ca 790 ms for 15-crown-5 it of ca 1 s and for acetate of ca 4 s. For the diffusion measurements on all the crown ether samples, the stimulated echo was used (see fig 1.6) and the parameters were set as following, the diffusion time Δ was set to 200 ms, the duration of gradient for sample 1-12 to δ = 1 ms, sample 13-24 to δ = 3 ms, the gradient strength g were increased linearly in 24 steps from 1 to 31 G.cm−1 using 4 scans and a relaxation delay D1 were 5 s. The delay was chosen to less then 5 ∗ T1(see eq 1.13,corresponds to less then 1% of magnetisation left in the xy plane). The experiment suitable for the acetate signal was set up in the same way as for the samples 13-24, with

17 the exception that the maximum gradient used was set to 18.5 G.cm−1 instead −1 of 31 G.cm and the relaxation time D1 was set to 20 s because of the longer relaxation time. In all electrophoretic measurements, the electrophoretic double stimulated echo was used (see fig 1.11 ). The duration of the magnetic field gradient δ was set to 1 ms, the diffusion time Δ was set to 200 ms, the gradient field strength g was for sample 1-12 set to 25 G.cm−1, sample 13-24 40 G.cm−1 was used and the potential difference was stepped up from 0 V to 400 V in 10 equal big steps. The 10 recorded spectrum were analysed for every sample and the phase differences between the peaks of crown ether and water was recorded. The phase difference between acetate and water was also calculated. Because of its known charge of (-1)(assuming no interactions with other species present), it was used as an extra insurance against systematic errors.

18 Chapter 3

Results and discussion

Below we presented the results illustrated with the data and ﬁtting performed in some representative samples

3.1 Diﬀusion measurements

In figure 3.1 the intensity of the 18-crown-6 peak is plotted against the magnetic field gradient for a sample containing 18-crown-6 and barium acetate, see sample number 6 table 2.1. By obtained the function given in eq 1.15, the diffusion coefficient can be calculated, in this case to 4.4 ∗ 10−10 m2.s−1(diffusion measurement typically have an error of 1 %). The diffusion in this case is significant lower than in the other cation systems and it depends on two factors: the high affinity and the relatively high molar mass (compared with the other cations) of barium 137.33 mol.l−1. In other words, the average 18-crown-6 molecule with barium attached is heavier.

3.2 Electrophoretic NMR

In figure 3.2 an example of data obtained in a crown ether cation system with poor affinity is shown, see sample number 13 table 2.1. The error of the measurement is large in relation to the phase shift, which results in a R2 value of 0.47. The electrophoretic mobility μ was fitted using eq 1.16 π ∗ 34.6 ∗ 100 ∗ (0.0044 ± 0.0075) μ = =(1.24 ± 2.1) ∗ 10−10 m2V −1s−1 26.75 ∗ 107 ∗ 40 ∗ 1 ∗ 0.2 ∗ 180 The effective charge (z) was calculated using eq 1.17

(1.24 ± 2.1) ∗ 10−10 ∗ 1.38 ∗ 10−23 ∗ 298 z = =0.0065 ± 0.011 4.76 ∗ 10−10 ∗ 1.602 ∗ 10−19 And the equilibrium constant (K) was calculated using eq 1.21

0.0065 −3 1 ∗ 10 ∗ 10 −1 K = 0.0065 2 −3 −3 =0.66 mol (1 − 1 ) ∗ 10 ∗ 10 ∗ 10 ∗ 10

19 Figure 3.1: Diﬀusion plot obtained in the 10 mM 18-crown-6 system with 10 mM barium acetate in D2O

Figure 3.2: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM lithium acetate in 10%/90% (v/v) H2O/D2O

20 Figure 3.3: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM barium acetate in 10%/90% (v/v) H2O/D2O

and log(K)=log(0.66) = −0.18 In figure 3.3 an example of a crown ether cation system with higher affinity is shown, see sample number 18 table 2.1. In this case, the phase shift is larger, so here the linear fit becomes much better than in the previous system. This results in a much better R2 value of 0.99946. In figure 3.4 an electrophoretic plot of 10 mM 18-crown-6 / 10 mM barium acetate, dissolved in D2O, see sample number 6 table 2.1. The following experiment was performed with a lower magnetic field gradient then in figure 3.3. If comparing the two plots a higher phase sift is achieved for the same applied voltage in figure 3.3 then in figure 3.4. In figure 3.5 the phase shift for the 15-crown-5, barium acetate system is shown, see sample number 24 table 2.1, the 15-crown-5 system with highest phase shift. All cations had a higher affinity to 18-crown-6 than 15-crown-5. The difference between the involved crown ethers is mainly the size of the cavity that has in, 18-crown-6 a diameter of 2.6-3.2 A˚ and in 15-crown-5 a diameter of 1.7-2.2 A.[24]˚

21 Figure 3.4: Electrophoretic phase shift for the crown ether signal recorded in the 18-crown-6 system with 10 mM barium acetate in D2O

Figure 3.5: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM barium acetate in 10%/90% (v/v) H2O/D2O

22 3.3 Summary of results

In table 3.1 - 3.2 the results from the samples solved in 10% H2O 90% D2O are shown. A more conventional method for measuring the equilibrium constant is calorime-

15-crown-5 Cation μ[m2/V s] D[m2/s] z[e] K[M −1] log(K) log(K)[11] log(K)[6] Li - 5.6E-10 - - - - - Na 6.2E-10 5.3E-10 0.030 ± 0.011 3.2 0.50 0.7 - K 3.0E-10 5.5E-10 0.014 ± 0.01 1.4 0.16 0.74 - Cs 4.4E-10 5.3E-10 0.021 ± 0.01 2.2 0.35 0.8 - Ca 9.4E-10 5.4E-10 0.045 ± 0.011 2.4 0.37 - - Ba 5.3E-09 5.3E-10 0.26 ± 0.013 17 1.2 1.71 -

Table 3.1: Summary of results with 15-crown-5 18-crown-6 Cation μ[m2/V s] D[m2/s] z[e] K[M −1] log(K) log(K)[11] log(K)[6] Li 1.2E-10 4.9E-10 0.0065 ± 0.011 0.66 -0.18 - - Na 1.1E-09 4.9E-10 0.056 ± 0.012 6.3 0.80 0.8 1 K 9.3E-09 4.8E-10 0.50 ± 0.017 200 2.3 2.03 2.1 Cs 1.7E-09 4.9E-10 0.088 ± 0.012 11 1.0 0.99 - Ca 1.3E-09 4.8E-10 0.067 ± 0.012 3.6 0.56 < 0, 5 1 Ba 2.7E-08 4.4E-10 1.6 ± 0.029 1800 3.3 3.87 3.6

Table 3.2: Summary of results with 18-crown-6 try, calorimetric studies are used here as reference data for the equilibrium constants [11, 6]. In comparison to calorimetric studies one advantage of electrophoretic NMR is that the equilibrium constant can be obtained for a system that already reached equilibrium, which is useful for systems that reach equilibrium fast. Another advantage is that the equilibrium constant can be derived for systems with more than one equilibrium taking place at the same time (assumed that the peaks do not overlap with each other and that there is only one charged compound in the system). Disadvantages with electrophoretic NMR is that at least one species that is included in the equation for the equilibrium constant has to be charged, and of course, it has to be NMR active. Advantages of calorimetric measurement are that the species do not need to be charged or NMR active. A disadvantage for calorimetric measurements is that the measurement has to be performed using pure reactants, there can be a problem if the reaction is very fast so that thermal gradients are produced, or very slow so that it can be hard to measure the heat ﬂux with good accuracy. The method can not give the equilibrium constants for systems with many chemical processes at the same time.

23 3.4 Sources of errors

A error which contributed to all electrophoretic NMR measurements on the Bruker Avance III 500 MHz was an artefact that distorted the baseline. The shape of the baseline changed as the voltage was increased. The problem sig- niﬁcantly increased the error of the measurement. The cause of the artefact is still unknown but it may have contributed to that the trend of the measured equilibrium constant deviates from the trend stated in the literature[11] for 15- crown-5 It still remains diﬃcult to explain the results for 15-crown-5 barium acetate and for 18-crown-6 barium acetate. In both cases the phase shift and precision was high. All electrophoretic measurements with barium acetate suggest a lower equilibrium constant then that obtained by calorimetry [11, 6]. The high phase shift eNMR measurement shod correspond to reliable data, so maybe the equilibrium constant from calorimetric measurement is not accurate enough.

24 Chapter 4

Conclusions

The investigation of these systems with Electrophoretic NMR shows a similar trend in cation affinity Ba>K>Cs>Na>Caas for 18-crown-6 in earlier calorimetric studies[11]. This is an indication that the eNMR technique is suitable for investigating thermodynamic properties for systems of similar kind. In previous investigation, around 3-4 degrees has been the error margin for the phase data in electrophoretic NMR measurement. If high accuracy is obtained an error less then 10%, a maximum phase shift higher then at least 30 degrees. At the maximum applied voltage is needed, which was not the case in every electrophoretic NMR measurement. This problem could be solved by tuning the experimental setup so that it allows an increase of those parameters that are connected to the size of the phase shift which are the duration of magnetic field gradient δ, diffusion time Δ, magnetic field gradient strength g and applied potential difference in the cell U.Unfor- tunately the increase of some of these parameters are at the expense of signal intensity (as in the case for increasing δ, Δ,g) or leads to strong sample heating (as in the case for increasing U ) A decrease of crown ether concentration would give a larger phase shift without increasing the total conductivity (because the phase shift corresponds to average charge of the crown ether which goes towards the charge of the cation as [crownether] the ratio of [cation] goes towards zero). But this would also lead to lower signal intensity. The parameter that allows higher signal intensity without negative consequences is an increase of the static field. The limitation is which type of spectrometer is available for the measurement at the given laboratory. The purpose of this thesis was to prove that electrophoretic NMR could be used to determine electrophoretic mobility and thermodynamic data. For crown ether cation systems, which is shown, because of that the same trend were establish as in the calorimetric studies[11], for the measurement were the phase shift at the maximum applied voltage was higher then 30o TheeNMRtechniquemakesit possible to derive information about how ions interacts with NMR active compounds. Properties such as electrophoretic mobility and equilibrium constant can be determined for not yet investigated systems.

25 Acknowledgements

First of all I want to thank prof Istv´an Fur´o for all his help and for letting me do my master thesis at physical chemistry. I also like to thank my supervisor Marianne Giesecke for teaching me how the operate the equipment and helping me when problems occurred. Finally I would like to thank every one at physical chemistry for your support and for nice conversation during Friday lunches.

26 Bibliography

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27 two isomers of dicyclohexo-18-crown-6 in aqueous solution at 25c degreec and mu = 0.1. Journal of the American Chemical Society, 98:7620–7626, 1976. [12] A. Jerschow and N. Müller. Suppression of convection artifacts in stimulated-echo diffusion experiments. double-stimulated-echo experiments. Journa of Magnetic Resonace, 125:372–375, 1997. [13] R. Kerssebaun. DOSY and diffusion by NMR. Bruker, 2002.

[14] J. Kowalewski and L. M´’aler. Nuclear spin relaxations in liquids: Theory, experements, and applications. Taylor and Francis, 2006. [15] M. H. Levitt. Spin dynamics. Basics of Nuclear Magnetic Resonance, chapter 20. John Wiley and Sons Ltd, 2008. [16] Y. Marcus. Ion properties, chapter 3. Marcel Dekker, Inc, 1997. [17] R. Mills. Self-diffusion in normal and heavy water in the range 1-45. The Journal of Physical Chemistry, 77:685–688, 1973. [18] C. J. Pedersen. Cyclic polyethers and their complexes with metal salts. Journal of the American Chemical Society, 89:2495–2496, 1967. [19] C. J. Pedersen. Crystalline salt complexes of macrocyclic polyethers. Jour- nal of the American Chemical Society, 92:386–391, 1970. [20] E. Pettersson, I. Furó, and P. Stilbs. On experimental aspects of electrophoretic nmr. Concepts in Magnetic Resonance, 22A:61–68, 2004. [21] W. S. Price. Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1 basic theory. Concepts in Magnetic Resonance, 9:299–336, 1997. [22] W. S. Price. NMR Studies of Translational Motion, chapter 2. Cambridge university press, 2009. [23] W. S. Price. NMR Studies of Translational Motion, chapter 6. Cambridge university press, 2009. [24] J. W. Steed and J. L. Atwood. Supramolecular Chemistry, chapter 3.1. John Wiley and Sons Ltd, 2000. [25] H. Tsukube. Double armed crown ethers and armed macrocycles as a new series of metal-selective reagents: a review. Talanta, 40:1313–1324, 1993.

28 Appendix

Here is all the electrophoretic NMR plot shown that was used to derive, the data in table 3.1 - 3.2

29 Figure A.1: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM lithium acetate in D2O

Figure A.2: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM sodium acetate in D2O

30 Figure A.3: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM potassium acetate in D2O

Figure A.4: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM caesium acetate in D2O

31 Figure A.5: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM calcium acetate in D2O

Figure A.6: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM barium acetate in D2O

32 Figure A.7: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM lithium acetate in D2O

Figure A.8: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM sodium acetate in D2O

33 Figure A.9: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM potassium acetate in D2O

Figure A.10: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM caesium acetate in D2O

34 Figure A.11: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM calcium acetate in D2O

Figure A.12: Electrophoretic phase shift for the crown ether signal recorded in the 18-crown-6 system with 10 mM sodium barium in D2O

35 Figure A.13: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM lithium acetate in 10%/90% (v/v) H2O/D2O

Figure A.14: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM sodium acetate in 10%/90% (v/v) H2O/D2O

36 Figure A.15: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM potassium acetate in 10%/90% (v/v) H2O/D2O

Figure A.16: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM caesium acetate in 10%/90% (v/v) H2O/D2O

37 Figure A.17: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM calcium acetate in 10%/90% (v/v) H2O/D2O

Figure A.18: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM barium acetate in 10%/90% (v/v) H2O/D2O

38 Figure A.19: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM lithium acetate in 10%/90% (v/v) H2O/D2O

Figure A.20: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM sodium acetate in 10%/90% (v/v) H2O/D2O

39 Figure A.21: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM potassium acetate in 10%/90% (v/v) H2O/D2O

Figure A.22: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM caesium acetate in 10%/90% (v/v) H2O/D2O

40 Figure A.23: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM calcium acetate in 10%/90% (v/v) H2O/D2O

Figure A.24: Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM barium acetate in 10%/90% (v/v) H2O/D2O

41 List of Figures

A.1 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM lithium acetate in D2O ...... 30 A.2 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM sodium acetate in D2O ...... 30 A.3 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM potassium acetate in D2O ...... 31 A.4 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM caesium acetate in D2O ...... 31 A.5 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM calcium acetate in D2O ...... 32 A.6 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM barium acetate in D2O ...... 32 A.7 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM lithium acetate in D2O ...... 33 A.8 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM sodium acetate in D2O ...... 33 A.9 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM potassium acetate in D2O ...... 34 A.10 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM caesium acetate in D2O ...... 34 A.11 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM calcium acetate in D2O ...... 35 A.12 Electrophoretic phase shift for the crown ether signal recorded in the 18-crown-6 system with 10 mM sodium barium in D2O ... 35 A.13 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM lithium acetate in 10%/90% (v/v) H2O/D2O ...... 36

42 A.14 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM sodium acetate in 10%/90% (v/v) H2O/D2O ...... 36 A.15 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM potassium acetate in 10%/90% (v/v) H2O/D2O ...... 37 A.16 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM caesium acetate in 10%/90% (v/v) H2O/D2O ...... 37 A.17 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM calcium acetate in 10%/90% (v/v) H2O/D2O ...... 38 A.18 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 15-crown-5 system with 10 mM barium acetate in 10%/90% (v/v) H2O/D2O ...... 38 A.19 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM lithium acetate in 10%/90% (v/v) H2O/D2O ...... 39 A.20 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM sodium acetate in 10%/90% (v/v) H2O/D2O ...... 39 A.21 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM potassium acetate in 10%/90% (v/v) H2O/D2O ...... 40 A.22 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM caesium acetate in 10%/90% (v/v) H2O/D2O ...... 40 A.23 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM calcium acetate in 10%/90% (v/v) H2O/D2O ...... 41 A.24 Electrophoretic phase shift for the crown ether (upper) and acetate (lower) signals recorded in the 18-crown-6 system with 10 mM barium acetate in 10%/90% (v/v) H2O/D2O ...... 41