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 István Furó

Stockholm June 29, 2012

Abstract

The purpose of this thesis was to investigate how crown ethers behave andinteract with different cations and to optimise the setup of the electrophoreticNMR. To get a good electrophoretic NMR measurement the electrophoreticphase shift needs to be big. To increase the phase shift some parameters neededto be adjusted, parameters such as the concentration of crown ether and cation,the duration of magnetic field gradient pulse δ, the magnetic field gradientstrength 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. Thecations used were lithium (Li), sodium (Na), potassium (K), caesium (Cs),calcium (Ca) and barium(Ba). The effective charge was obtained by using pulsedgradient NMR to derive the diffusion coefficient and electrophoretic NMR to getthe electrophoretic mobility. These data were used to calculate the equilibriumconstant of the formed complex.The outcome of the investigation: the affinity for 18-crown-6 was in the followingorder

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 f̊a en bra elektroforetiska NMR mätning måste fasskiftet vara stort.För att öka fasskiftet behövs n̊agra parametrar ställas in s̊a som koncentrationav kroneter och katjon, längden av magnetfältsgradientspulsen δ, den gradi-entstyrkan g, diffusionstiden Δ och den applicerade spänningen V.Fokus har lagts p̊a kronetrarna 15-kron-5 och 18-krona-6. De använda katjonervar litium (Li), natrium (Na), kalium (K), cesium (Cs), kalcium (Ca) och bar-ium (Ba).De olika systemen undersöktes med hjälp av diffusions NMR för att mäta diffu-sionskoefficienten och elektroforetisk NMR för att f̊a 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 för 15-kron-5

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

ii

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iSammanfattning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

1 Background 11.1 Crown ethers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Acetate salts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Electrophoresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Different types of NMR techniques . . . . . . . . . . . . . . . . . 3

1.4.1 Conventional NMR . . . . . . . . . . . . . . . . . . . . . . 31.4.2 Pulsed field gradient NMR . . . . . . . . . . . . . . . . . 61.4.3 Electrophoretic NMR . . . . . . . . . . . . . . . . . . . . 10

2 Summary of research 142.1 Assembling of the electrophoretic cell . . . . . . . . . . . . . . . . 142.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Calibration of the electrophoretic cell . . . . . . . . . . . 142.2.2 Calibration of the diffusion measurement . . . . . . . . . 152.2.3 Calibration of the gradient . . . . . . . . . . . . . . . . . 16

2.3 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Results and discussion 193.1 Diffusion measurements . . . . . . . . . . . . . . . . . . . . . . . 193.2 Electrophoretic NMR . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 Sources of errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 manystudies have been using electrophoretic NMR. Crown ethers are of interest be-cause their properties are useful in applications such as catalysts for chemicalreactions [1], phase transfer reagents, increasing solubility of salts in organicliquids [19], hosts for transport across membranes [3] and separation processes[25].To investigate the interaction between crown ethers and cations, three differentNMR techniques were used: conventional NMR, pulsed field gradient NMR andelectrophoretic NMR.Conventional NMR uses the magnetic moment of nuclei, to derive informationabout their surroundings.In pulsed gradient NMR magnetic field gradients are applied to achieve a lossin signal strength of the peaks in the spectra. The behaviour of the decayingsignal can be used to derive the diffusion coefficientElectrophoretic NMR is a combination between electrophoresis and pulsed gra-dient NMR and measures phase shift in the spectra under increasing electricfield and constant magnetic field gradient. If the diffusion coefficient is knownthen the technique makes it possible to derive information like: electrophoreticmobility, 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]. Thisdiscovery later gave him the Nobel prize in 1987 together with Jean-Marie Lehnand 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 moleculardipole moment the chain folds into something that reminds of a crown, hencethe name. The closed structure gives rise to a cavity and this is the origin of itsinteresting properties, such as binding to different cations. These phenomenacan exist thanks to the interaction between the oxygen atoms in the crown etherand 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 thecomplex and cation, size of the cation and the crown ether. The size selectivitytends to decrease as the ring size of the crown ether increases, since it is easierfor a larger ether to achieve a folded configuration to optimise its interactionwith the cation, because of the high flexibility.[24, 11]The sum of the thermodynamic effects gets reflected in the equilibrium constant

K =[crown ether cation complex]

[free cation][unoccupied crown ether]. (1.1)

The equilibrium constant varies with the cation, which makes it possible to sep-arate cations from each other by using a crown ether that is selective to one ofthe cations in the system [25].Other applications for crown ethers are catalysts for chemical reactions [1], phasetransfer 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 cavitysizes of approximately 1.3-1.7 Å respectively 0.9-1.1 Å, see Figure 1.1.

1

(a)15crown5

O O

O

O

O

(b)18crown6

O

O

O

OO

O

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 canbe easily detected by 1H NMR.The cations to acetate explored here are listed in Table 1.1 together with theirrespective ionic radius [16]

Cation Ionic radius [Å]Li+ 0.69Na+ 1.02K+ 1.38Cs+ 1.70Ca2+ 1.00Ba2+ 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 influ-enced by a force [9]

Fe =qU

l, (1.2)

where Fe is the force in [N], q is charge of the particle in [C], U is the electricpotential difference in [V] and l is the distance between the electrodes in [m].This phenomenon is explored in electrophoresis. If the particle is not movingin vacuum, its movement interferes with the surrounding medium which corre-sponds to a friction force that is acting to restrict motion. The friction force isdependent of the speed and the interaction between the particle and the mediumand is given by the equation:

Ff = fv (1.3)

2

where Ff is the friction force in [N], f the friction coefficient in [Nsm−1] and v

the velocity in [ms−1].When the two forces are equal then the acceleration stops and the particletravels at a constant speed which gives the following expression.

v =qU

lf(1.4)

The self motion of a system in a medium is called diffusion and it depends onthe thermal energy of the systems and the resistance against movement. Thediffusion is described by the Einstein-Sutherland equation:

D =kBT

f, (1.5)

where D is the diffusion coefficent in [m2s−1], kB is the Boltzmann factor in[JK−1] and T is the temperature in [K].By combining eq 1.4 and eq 1.5 the following expression can be derived.

D =vkBT l

qU(1.6)

The definition of electrophoretic mobility is

μ =vl

U(1.7)

which makes it possible to express the diffusion coefficient in the following way[7]

D =μkBT

q. (1.8)

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 struc-ture, diffusion properties and electrophoretic mobility for different NMR activesubstances. [21, 7, 10]

1.4.1 Conventional NMR

NMR exploit the nuclear spin properties of different atoms, which is usefulto determine the local environment surrounding every NMR active nuclei. Inorder not to violate basic quantum mechanic, the spin of the nuclei, denoted byI, has to be quantized, as described by the magnetic quantum number mI . In amagnetic field the different magnetic quantum numbers correspond to differentenergies [10]

E =mIγhB

2π(1.9)

where E is energy in [J], B the magnetic field strengthen at the site of theactive nuclei in [Tesla(T )], γ is the gyromagnetic ratio [s−1T−1] and h is Planckconstant [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 theorientation of the static magnetic field (called thermal equilibrium).Transitions between states with different magnetic quantum number ΔmI = 1give by equation[10]

ΔE =γhB

2π. (1.10)

Because of the relationΔE = hω (1.11)

where ω is a frequency in [Hz],combining 1.10 and 1.11, yields the so called Larmor frequency [10]

ω =γB

2π(1.12)

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 fre-quency. This induces a torque on the net magnetization and it turns it awayfrom its equilibrium. The resulting orientation of the net magnetization relativeto the static field depends of the intensity of the applied radio frequency pulseand its duration. Most common is to use pulses that turn the net magnetiza-tion 90o and 180o. The maximum detectable signal occurs after a 90o pulse, seefig 1.2, because then all the magnetisation is in the xy plane where it is possibleto detect. [22]Nuclei of the same type of isotope in the same spectrometer can have differentLarmor frequency, because eq 1.12 is dependent on magnetic field. And thereis a slight difference, depending on their close environment and especially thedensity of electrons surrounding the nuclei, a high density of electrons has atendency to shield the magnetic field, so the sensed magnetic field will be lessthan the applied, and this makes it possible to separate signals from differentmolecules. Of the same reason, it is possible to collect information about thenuclei 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 approachsaves a lot of time which makes it possible to get a better signal to noise ratioin loss of time.[4]

4

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

To get the FID (free induction decay), see 1.2, the voltage that is introduced bythe time dependent magnetisation in the xy-plane needs to be plotted againsttime. Transformation from time domain to frequency domain (so called Fouriertransform) creates a one-dimensional chemical shift dependent spectrum, seefig 1.3. [2]Two properties that are important to consider when measuring are the longi-tudinal (T1) and transverse (T2) relaxation.Longitudinal relaxation time is a measure of how fast the system reaches ther-mal equilibrium after having been excited. The process is typically described as[5]

Δn(t) = Δneq

[1− exp

(− tT1

)](1.13)

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 relax-ation time in [s].The pulse program inversion recovery (see fig 1.4) can be used for measuringT1.Transverse relaxation time is a measure how fast the magnetic component

perpendicular to the static field is lost.Both relaxation times are influenced bymolecular dynamics in the chemical system. [15]The reason for relaxation is fluctuations in the magnetic field.[10] Mechanismsthat give short relaxation times are quadrupolar and paramagnetic relaxation.Quadrupolar relaxation occurs only for nuclear spins higher then 12 . Paramag-netic relaxation occurs when a nucleus with spin 12 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 ofkeeping B0 field constant it is made dependent on the position along the z-axis(same direction as the B0 magnetic field)

dBzdz �= 0.

Two commonly used pulse programs are the spin-echo and stimulated echo, seefig 1.5 and fig 1.6. A difference between the two pulse programs is in whichdirection the magnetisation is stored under the principal duration of the pulseprogram, so the choice of pulse program depends on the T1 and T2 relaxationof the investigated sample. Stimulated echo tends to give less artefacts in themeasurement and therefore it is the most commonly used. There also existsa double stimulated echo which is a combination of two stimulated-echo pulseprograms after each other.The Larmor frequency of the nucleus see, eq 1.12, is dependent on the magneticfield. By applying a magnetic field gradient the Larmor frequency of the nu-cleus becomes dependent on position along the gradient. This can be used tofollow compounds that move randomly (called self diffusion) in between the twogradient pulses. The change in environment corresponds to an offset of the Lar-mor frequency. The magnitude of the offset is dependent on the gyromagneticratio, the gradient field strength, the duration of the magnetic field pulse andthe difference at the times of the two magnetic field gradient pulses accordingto 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 aconfined space in any direction) the Stejskal-Tanner equation is valid

S

S0= exp

[−γ2δ2g2D

(Δ− δ

3

)](1.15)

where S is the signal intensity with magnetic field gradient applied, S0 is thesignal 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-6and 10 mM barium acetate dissolved in D2O. The peaks corresponds to, fromthe left, water, crown ether and acetate

ratio in [s−1T−1], δ is the duration of magnetic field gradient pulse in [s], gis 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 ofthe variables are constant, the diffusion coefficient can be calculated accordingto equation 1.15. For more detailed information see ref [21]. In fig 1.8 the signalintensity is plotted as a function of the magnetic field gradientIf 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 withoutany 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 diffusionNMR. For being able to achieve the fusion of the two techniques the NMR cellneeds to be modified. Hence two electrodes had been added into a 5 mm NMRtube, see fig 1.12. The modification made it possible to apply a potential dif-ference over the sample length. The generated electric field, is responsible fora 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. Theexperiment is usually set up in that manner that positive species gives positivephase shift and negative specie give a negative phase shift, but this is just amatter of convention.Because of the applied electric field, the pulse program used in diffusion NMRalso needs to be modified. In fig 1.11, a pulse program of an electrophoreticdouble stimulated echo is shown. It is quite similar to an ordinary double stim-ulated echo mentioned in the pulsed gradient NMR part, fig 1.9. Here twoelectrophoretic pulses are included, the direction of the electric field is switchedto the opposite after half the diffusion time Δ2 .The pulse program has the advantage to suppresses phase shifts as an artefact ofthermal convection. This is possible because thermal convection is independenton the electric field. For a more detailed explanation, see [7] and [12]There are additional effects that influence the bulk flow (and the electrophoreticdouble stimulated echo cannot suppress all convection effects). This makes itimportant to keep track on the movement of uncharged species, because thesespecies can be used as a reference of how the bulk is flowing. By subtractingthe phase shift of the charged compounds from that of the uncharged, once thetuned electrophoretic phase shift can be derived. In this thesis water was usedas reference.[7] If the phase shift is plotted as a function of applied voltage, (seefig 1.10), the slope can be used to derive the electrophoretic mobility, accordingto the following equation

μ =l

γgδΔ

φ

U(1.16)

where μ is electrophoretic mobility in [m2V −1s−1], l is the distance between thetwo electrodes in [m], γ is the gyromagnetic ratio in [s−1T−1], g is the magneticfield gradient in [Tm−1],δ diffusion time in [s], Δ is the duration of the gradientpulse in [s], φ is the phase shift in [rad] and U the applied voltage in [V ].When the electrophoretic mobility is known, it is possible to calculate the effec-tive charges z

z =μkBT

De(1.17)

where kB Boltzmann constant in [JK−1], T the temperature in [K] and e the

elementary charge in [C].

10

Figure 1.10: Spectra recorded in an electrophoretic NMR experiment plottedagainst applied voltage, for a system consisting of 10 mM 18-crown-6, 10 mMbarium acetate dissolved in D2O. The peaks correspond, from the left, waterand 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 ofcrown ether to calculate the concentration of cation crown ether complexes atequilibrium looks like following

[crown ether cation complex] =z

n[crown ether]. (1.18)

were n is the nominal charge of the cation, z the effective charge of the crownether 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 con-centration of cation crown ether complexes at equilibrium gives the free crownether concentration at equilibrium

[unoccupied crown ether] = [crown ether]− zn[crown ether] =

= (1 − zn)[crown ether] (1.19)

and similar for the free cation concentration at equilibrium

[free cation] = [Xn]− zn[crown ether]

were [X ] is the starting concentration of the cation in [mol l−1]. If the ratiois 1:1 between [Xn] and [crown ether] as it was in this thesis the free cationconcentration at equilibrium can modified

[free cation] = [Xn]− zn[Xn] = (1 − z

n)[Xn]. (1.20)

By modifying eq 1.1 using eq 1.18-1.20 following expression for the equilibriumconstant can be derived

K =zn [crown ether]

(1− zn )2[crown ether][Xn]. (1.21)

[7]

12

Figure 1.11: The electrophoretic double stimulated echo (EPGDSTE) pulsesequence [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 accuratedata.

2.2.1 Calibration of the electrophoretic cell

To calculate the electrophoretic mobility, the distance between the two elec-trodes in the cell must be determined (see fig 1.12). This is done by measuringthe phase shift at different applied voltages. For a sample with known elec-trophoretic mobility.A 10mM tetramethylammonium bromide (≥ 99.0 %, Merck) (N(CH3)4Br) so-lution in D2O (99.9 atom% D, Isotec inc) was used for this purpose. Themeasurement was performed three times and the solution was changed eachrun. The pulse program used was an electrophoretic double-stimulated echodeveloped py Pettersson et al [20], see fig 1.11, the duration of the magneticfield gradient δ was set to 1 ms, the diffusion time Δ to 200 ms, the gradientfield strength g to 25 Gcm−1 and the potential difference was stepped up from0 V up to 400 V in 10 equal steps.By using equation 1.16 and rearranging the parameters, the distance betweenthe two electrodes was given by the relation:

l = μγgδΔ

[φ

U

]−1

The average length was obtained as.

l̄ =μγgδΔ

3

{[φ

U

]−11

+

[φ

U

]−12

+

[φ

U

]−13

}

14

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

By using the known electrophoretic mobility and the average slope of the mea-surement, see fig 2.1, the length could be calculated as.

l̄ =180

π

3.749 ∗ 10−8 ∗ 26.75 ∗ 107 ∗ 53.5 ∗ 0.9 ∗ 0.52 ∗ 0.2 ∗ 10−3100

×

×{[0.8172]−1 + [0.8358]−1 + [0.8391]−1

3

}= 0.0346m

180π is a conversion constant to transform degrees into radians.The standard deviation was calculated as

±s = μγgδΔ

√√√√√([

φU

]−11

− ¯[φU

]−1)2+

([φU

]−12

− ¯[φU

]−1)2+

([φU

]−13

− ¯[φU

]−1)22

=

= ±0.000496mThe value 34.6± 0.5 mm was then used as the length between the electrodes inall 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 coefficientof 1.889 ∗ 10−9m2s−1 which was compared with published data for the samesystem 1.902 ∗ 10−9m2s−1 [17]. The ratio between D0Dmeasured was 1.00688, everymeasured 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

g = gapp

√DappD0

(2.1)

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

2.3 Sample preparation

The following chemicals were used during the whole project lithium(I) ac-etate (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 cationconcentration 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 improvethe 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 andelectrophoretic measurements of the samples 1-12, were performed on a BrukerAvance 500 MHz using a BB inverse probe with z-gradient and maximum mag-netic field gradient 51.3 G.cm−1. The diffusion and electrophoretic measure-ments of the samples 13-24, were performed on a Bruker Avance III 500 MHzusing a diff 30 z-gradient probe with maximum magnetic field gradient 1800G.cm−1.The first step were to prepare four 10 mM solutions consisting of the two dif-ferent crown ethers solved in the two solvents, the concentration was tuned byusing the integral in a 1H NMR spectra the reference used consisted of an 100mM tetramethylammonium bromide solution solved in D2O.(This procedurewas necessary because of former experiment resulted in that the integral showna different relation between the cation and the crown ether then the measuredweight.) The concentration of the four crown ether solutions were tuned untilthe concentration corresponded to 10 mM.These four samples were then used for dissolving the following salts: lithiumacetate, sodium acetate, potassium acetate, caesium acetate, calcium acetate

16

SamplesSample number Salt Crown ether Solvent

1 Li acetate 18-crown-6 D2O2 Na acetate 18-crown-6 D2O3 K acetate 18-crown-6 D2O4 Cs acetate 18-crown-6 D2O5 Ca acetate 18-crown-6 D2O6 Ba acetate 18-crown-6 D2O7 Li acetate 15-crown-5 D2O8 Na acetate 15-crown-5 D2O9 K acetate 15-crown-5 D2O10 Cs acetate 15-crown-5 D2O11 Ca acetate 15-crown-5 D2O12 Ba acetate 15-crown-5 D2O13 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 saltconcentration of the solutions were tuned by 1H NMR spectra until a devia-tion from an 1:1 molar relation between the crown ether and the cation was lessthan 5 %. This procedure was necessary because of the calculated concentrationbased on the weighed mass of the salts were not accurate, due to the hygroscopicproperties of the salts.Two T1 measurements were performed on the sample number 3 to derive T1 for18-crown-6, acetate and sample number 7 to get T1 for 15-crown-5. The pulsewas inversion recovery (see fig 1.4). The purpose of the two measurements wereto optimise the parameters for the upcoming diffusion and electrophoretic mea-surement. The results gave a T1 for 18-crown-6 of ca 790 ms for 15-crown-5 itof ca 1 s and for acetate of ca 4 s.For the diffusion measurements on all the crown ether samples, the stimulatedecho was used (see fig 1.6) and the parameters were set as following, the dif-fusion time Δ was set to 200 ms, the duration of gradient for sample 1-12 toδ = 1 ms, sample 13-24 to δ = 3 ms, the gradient strength g were increasedlinearly in 24 steps from 1 to 31 G.cm−1 using 4 scans and a relaxation delayD1 were 5 s. The delay was chosen to less then 5 ∗ T1(see eq 1.13,correspondsto less then 1% of magnetisation left in the xy plane). The experiment suitablefor 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 insteadof 31 G.cm−1 and the relaxation time D1 was set to 20 s because of the longerrelaxation time.In all electrophoretic measurements, the electrophoretic double stimulated echowas used (see fig 1.11 ). The duration of the magnetic field gradient δ was set to1 ms, the diffusion time Δ was set to 200 ms, the gradient field strength g wasfor sample 1-12 set to 25 G.cm−1, sample 13-24 40 G.cm−1 was used and thepotential difference was stepped up from 0 V to 400 V in 10 equal big steps. The10 recorded spectrum were analysed for every sample and the phase differencesbetween the peaks of crown ether and water was recorded.The phase difference between acetate and water was also calculated. Because ofits 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 performedin some representative samples

3.1 Diffusion measurements

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

3.2 Electrophoretic NMR

In figure 3.2 an example of data obtained in a crown ether cation system withpoor affinity is shown, see sample number 13 table 2.1. The error of the mea-surement is large in relation to the phase shift, which results in a R2 value of0.47.The electrophoretic mobility μ was fitted using eq 1.16

μ =π ∗ 34.6 ∗ 100 ∗ (0.0044± 0.0075)26.75 ∗ 107 ∗ 40 ∗ 1 ∗ 0.2 ∗ 180 = (1.24± 2.1) ∗ 10

−10 m2V −1s−1

The effective charge (z) was calculated using eq 1.17

z =(1.24± 2.1) ∗ 10−10 ∗ 1.38 ∗ 10−23 ∗ 298

4.76 ∗ 10−10 ∗ 1.602 ∗ 10−19 = 0.0065± 0.011

And the equilibrium constant (K) was calculated using eq 1.21

K =0.0065

1 ∗ 10 ∗ 10−3(1− 0.00651 )2 ∗ 10 ∗ 10−3 ∗ 10 ∗ 10−3

= 0.66mol−1

19

Figure 3.1: Diffusion plot obtained in the 10 mM 18-crown-6 system with 10mM 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 acetatein 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 acetatein 10%/90% (v/v) H2O/D2O

andlog(K) = log(0.66) = −0.18

In figure 3.3 an example of a crown ether cation system with higher affinity isshown, 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. Thisresults 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 ex-periment 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 appliedvoltage in figure 3.3 then in figure 3.4. In figure 3.5 the phase shift for the15-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 differencebetween the involved crown ethers is mainly the size of the cavity that has in,18-crown-6 a diameter of 2.6-3.2 Å and in 15-crown-5 a diameter of 1.7-2.2 Å.[24]

21

Figure 3.4: Electrophoretic phase shift for the crown ether signal recorded inthe 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 acetatein 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% D2Oare shown.A more conventional method for measuring the equilibrium constant is calorime-

15-crown-5Cation 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-6Cation 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 1K 9.3E-09 4.8E-10 0.50± 0.017 200 2.3 2.03 2.1Cs 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 1Ba 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 con-stants [11, 6].In comparison to calorimetric studies one advantage of electrophoretic NMR isthat the equilibrium constant can be obtained for a system that already reachedequilibrium, which is useful for systems that reach equilibrium fast. Anotheradvantage is that the equilibrium constant can be derived for systems with morethan one equilibrium taking place at the same time (assumed that the peaksdo not overlap with each other and that there is only one charged compound inthe system).Disadvantages with electrophoretic NMR is that at least one species that is in-cluded in the equation for the equilibrium constant has to be charged, and ofcourse, it has to be NMR active.Advantages of calorimetric measurement are that the species do not need to becharged or NMR active. A disadvantage for calorimetric measurements is thatthe measurement has to be performed using pure reactants, there can be a prob-lem if the reaction is very fast so that thermal gradients are produced, or veryslow so that it can be hard to measure the heat flux with good accuracy. Themethod can not give the equilibrium constants for systems with many chemicalprocesses at the same time.

23

3.4 Sources of errors

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

24

Chapter 4

Conclusions

The investigation of these systems with Electrophoretic NMR shows a similartrend in cation affinity Ba > K > Cs > Na > Ca as for 18-crown-6 in earliercalorimetric studies[11]. This is an indication that the eNMR technique is suit-able for investigating thermodynamic properties for systems of similar kind.In previous investigation, around 3-4 degrees has been the error margin for thephase data in electrophoretic NMR measurement. If high accuracy is obtainedan 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 everyelectrophoretic NMR measurement.This problem could be solved by tuning the experimental setup so that it allowsan increase of those parameters that are connected to the size of the phase shiftwhich are the duration of magnetic field gradient δ, diffusion time Δ, magneticfield 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 signalintensity (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 withoutincreasing the total conductivity (because the phase shift corresponds to aver-age charge of the crown ether which goes towards the charge of the cation as

the ratio of [crownether][cation] goes towards zero). But this would also lead to lower

signal intensity.The parameter that allows higher signal intensity without negative consequencesis an increase of the static field. The limitation is which type of spectrometeris available for the measurement at the given laboratory.The purpose of this thesis was to prove that electrophoretic NMR could be usedto determine electrophoretic mobility and thermodynamic data. For crown ethercation systems, which is shown, because of that the same trend were establish asin the calorimetric studies[11], for the measurement were the phase shift at themaximum applied voltage was higher then 30o The eNMR technique makes itpossible to derive information about how ions interacts with NMR active com-pounds. Properties such as electrophoretic mobility and equilibrium constantcan be determined for not yet investigated systems.

25

Acknowledgements

First of all I want to thank prof István Furó for all his help and for letting medo my master thesis at physical chemistry.I also like to thank my supervisor Marianne Giesecke for teaching me how theoperate the equipment and helping me when problems occurred.Finally I would like to thank every one at physical chemistry for your supportand for nice conversation during Friday lunches.

26

Bibliography

[1] J. Almy, D. C. Garwood, and Donald J. Cram. Electrophilic substitution atsaturated carbon. xliv. stereochemical and isotopic drowning phenomenal.Journal of the American Chemical Society, 92:4321–4330, 1970.

[2] D. Canet and P. Mutzenhardt. Encyclopedia of Analytical Chemistry, chap-ter Relaxation in Nuclear Magnetic Resonance, General. John Wiley andSons Ltd, 2006.

[3] A. Casnati, A. Pochini, R. Ungaro, J. F. Ugozzoli, F. Arnaud, S. Fanni,M.J. Schwing, *R. J. M. Egberink, F. de Jong, and D. N. Rein-houdt. Synthesis, complexation, and membrane transport studies of 1,3-alternate calix[4]arene-crown-6 conformers: A new class of cesium selectiveionophores. Journal of the American Chemical Society, 117:2767–2777,1995.

[4] R. R. Ernst and W. A Anderson. Application of fourier transform spec-troscopy to magnetic resonance. The Review of Scientific Instruments,37:93–102, 1966.

[5] T. C. Farrar and E. D. Becker. Pulse and Fourier transform NMR. In-toduction to theory and methods. Academic press New York and London,1971.

[6] C. Francois, Ph. Morin, and M. Dreux. Effect of the concentration of18-crown-6 added to the electrolyte upon the separation of ammonium,alkali and alkaline-earth cations by capillary electrophoresis. Journal ofChromatography A, 706:535–553, 1995.

[7] F. Hallberg. Molecular interactions studied by Electrophoretic and diffusionNMR. PhD thesis, KTH, 2010.

[8] F. Hallberg, I. Furó, P.V. Yushmanov, and P. Stilbs. Sensitive and ro-bust electrophoretic nmr: Instrumentation and experiments. Journal ofMagnetic Resonance, 192:69–77, 2008.

[9] D. Halliday and R. Resnick. Physics, chapter 27. John Wiley and SonsLtd, 1978.

[10] P.J. Hore. Nuclear Magnetic Resonance. Oxford science publications, 1995.

[11] R.M. Izatt, R.E. Terry, B.L. Haymore, L.D. Hansen, N.K. Dalley, A.G.Avondet, and J.J. Christensen. Calorimetric titration study of the inter-action of several uni- and bivalent cations with 15-crow-5,18-crown-6, and

27

two isomers of dicyclohexo-18-crown-6 in aqueous solution at 25c degreecand mu = 0.1. Journal of the American Chemical Society, 98:7620–7626,1976.

[12] A. Jerschow and N. Müller. Suppression of convection artifactsin stimulated-echo diffusion experiments. double-stimulated-echo experi-ments. 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, chap-ter 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. TheJournal 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 elec-trophoretic nmr. Concepts in Magnetic Resonance, 22A:61–68, 2004.

[21] W. S. Price. Pulsed-field gradient nuclear magnetic resonance as a tool forstudying translational diffusion: Part 1 basic theory. Concepts in MagneticResonance, 9:299–336, 1997.

[22] W. S. Price. NMR Studies of Translational Motion, chapter 2. Cambridgeuniversity press, 2009.

[23] W. S. Price. NMR Studies of Translational Motion, chapter 6. Cambridgeuniversity 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 newseries 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, thedata 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein D2O

Figure A.12: Electrophoretic phase shift for the crown ether signal recorded inthe 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 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 acetatein 10%/90% (v/v) H2O/D2O

41

List of Figures

A.1 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM lithium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 30

A.2 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM sodium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 30

A.3 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM potassium acetate in D2O . . . . . . . . . . . . . . . . . . . 31

A.4 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM caesium acetate in D2O . . . . . . . . . . . . . . . . . . . . 31

A.5 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM calcium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 32

A.6 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM barium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 32

A.7 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM lithium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 33

A.8 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM sodium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 33

A.9 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM potassium acetate in D2O . . . . . . . . . . . . . . . . . . . 34

A.10 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM caesium acetate in D2O . . . . . . . . . . . . . . . . . . . . 34

A.11 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM calcium acetate in D2O . . . . . . . . . . . . . . . . . . . . . 35

A.12 Electrophoretic phase shift for the crown ether signal recorded inthe 18-crown-6 system with 10 mM sodium barium in D2O . . . 35

A.13 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM lithium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 36

42

A.14 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM sodium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 36

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

A.16 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM caesium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 37

A.17 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM calcium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 38

A.18 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 15-crown-5 system with 10mM barium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 38

A.19 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM lithium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 39

A.20 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM sodium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 39

A.21 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM potassium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . 40

A.22 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM caesium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 40

A.23 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM calcium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 41

A.24 Electrophoretic phase shift for the crown ether (upper) and ac-etate (lower) signals recorded in the 18-crown-6 system with 10mM barium acetate in 10%/90% (v/v) H2O/D2O . . . . . . . . 41

43

AbstractSammanfattningContentsIntroductionBackgroundCrown ethersAcetate saltsElectrophoresisDifferent types of NMR techniquesConventional NMRPulsed field gradient NMRElectrophoretic NMR

Summary of researchAssembling of the electrophoretic cellCalibrationCalibration of the electrophoretic cellCalibration of the diffusion measurementCalibration of the gradient

Sample preparation

Results and discussionDiffusion measurementsElectrophoretic NMRSummary of resultsSources of errors

ConclusionsAcknowledgementsBibliographyAppendixList of figures