Methyl Quantum Tunneling and Nitrogen-14 NQR NMR Studies Using a SQUID Magnetic Resonance Spectrometer

TL;DR: In this article, a new spectrometer with a dc SQUID (Superconducting Quantum Interference Device) detector, which has no such frequency dependence, has been developed.

Abstract: Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR) techniques have been very successful in obtaining molecular conformation and dynamics information. Unfortunately, standard NMR and NQR spectrometers are unable to adequately detect resonances below a few megahertz due to the frequency dependent sensitivity of their Faraday coil detectors. For this reason a new spectrometer with a dc SQUID (Superconducting Quantum Interference Device) detector, which has no such frequency dependence, has been developed. Previously, this spectrometer was used to observe {sup 11}B and {sup 27}Al NQR resonances. The scope of this study was increased to include {sup 23}Na, {sup 51}V, and {sup 55}Mn NQR transitions. Also, a technique was presented to observe {sup 14}N NQR resonances through cross relaxation of the nitrogen polarization to adjacent proton spins. When the proton Zeeman splitting matches one nitrogen quadrupoler transition the remaining two {sup 14}N transitions can be detected by sweeping a saturating rf field through resonance. Additionally, simultaneous excitation of two nitrogen resonances provides signal enhancement which helps to connect transitions from the same site. In this way, nitrogen-14 resonances were observed in several amino acids and polypeptides. This spectrometer has also been useful in the direct detection of methyl quantum tunneling splittingsmore » at 4.2 K. Tunneling, frequencies of a homologous series of carboxylic acids were measured and for solids with equivalent crystal structures, an exponential correlation between the tunneling frequency and the enthalpy of fusion is observed. This correlation provides information about the contribution of intermolecular interactions to the energy barrier for methyl rotation.« less

Summary

Chapter 1 Introduction

• Magnetic resonance has become an important tool in the modem scientist's arsenal for the determination of structural and dynamical information.
• Solid state NMR and NQR are used to examine this interaction.
• Typical NQR experiments can measure large quadrupolar couplings of nuclei such as the halogens.
• This spectrometer uses a dc SQUID 1416 (Superconducting Quantum Interference Device) as a detector of magnetic resonance signals.
• The theory and results of these experiments are presented in Chapter 5.

Chapter 2 The SQUID Magnetic Resonance Spectrometer

• This chapter focuses on a brief description of the dc SQUID and the SQUID spectrometer.
• Both of these subjects are presented in greater detail elsewhere, 15 ' 17, 18,21, 27-36 my purpose is simply to provide a working knowledge of the spectrometer and the SQUID that will allow one to understand the experiments in this thesis.
• Because the SQUID is a device designed to use the unique properties of a superconductor in a magnetic field I will begin this chapter with a discussion of that subject including descriptions of the Meisner effect or flux exclusion, flux trapping and quantization, and the .
• The second part of the chapter will introduce the theory behind the operation of a dc SQUID and explain how it can be used as a magnetic resonance detector.
• The third section will present a survey of the spectrometer and outline several recent changes in operation.

2.1 Superconductivity in a Magnetic Field

• 37 Thus was born the study of superconductors.
• These sets of electrons became known as Cooper pairs.
• In this thesis I will be concerned only with materials that do act in accordance with the BCS theory.
• When superconductors are placed in a magnetic field, it was found that they can be classified into two distinct types.
• Between the two critical fields, parts of the sample become nonsuperconducting.

2.1.1 Flux Exclusion: The Meisner Effect

• When a magnetic field is applied around a superconductor, the material generates currents to oppose the field according to Lenz's law.
• Because there is no resistance in the superconducting state, these persistent currents will eliminate the magnetic field in the interior of the superconductor.
• Thus magnetic flux is excluded from the material except for a narrow region near the surface, the depth of which is calculated below.
• More interesting is the related phenomenon discovered experimentally by Meisner and depicted in Figure 2 .1. 40.
• The explanation of this result can be found by first developing the London equation.

2.1.2 Flux Trapping and Quantization

• Something interesting happens if, instead of a solid sample, a ring of superconducting material is placed into a magnetic field at high temperature and cooled below TC .43.
• Even when the magnetic field is removed the flux through the ring remains constant, as depicted in Figure 2 .1, and is quantized.
• The authors use this property to provide a small steady field for their magnetic resonance experiments.
• The authors start with equation 2.5; 1 Let's examine a closed path C through the interior of the superconductor but well away from the surface.
• The authors know from the previous section that B and thus j "-re zero in this region.

2.2.1 Fundamental

• The dc SQUID in their detector contains two parallel Josephson junctions; a and b, a magnetic flux, OL, penetrating the loop; a potential, V, across the junctions; and a current, Jb' biasing the SQUID.
• A supercurrent is generated through the Josephson junctions as described above which can be separated into two parts, one component going between points P and Q through junction a and the other going through junction b.
• Each part of the supercurrent will gain a phase due to both the.

2.2.2 The SQUID as a Detector

• There are several simple ways in which the SQUID can be used as a detector.
• With this advantage the authors want to use the SQUID to detect low frequency (down to dc) signals.
• This higher frequency signal can then be detected with only the typical white noise.
• The amount of flux ultimately coupled into the SQUID depends on the mutual inductance between the coupling coil and the SQUID, Mcs, as given by Mes *(4g2fr2pNpM).
• 49, 50 The actual dependence is greater when it is realized that for larger samples the filling factor is better because the walls of the sample container are usually kept constant.

2.3.1 Hardware Overview

• The rf field is on during detection and is coupled by mutual inductance into the pickup coil.
• Thus, a low pass filter must be used to eliminate the coupled rf and retain the signal (which is near dc).
• This places a limit on the rf frequency that can be used for irradiation.
• Also, a lead lined brass can surrounds the coil form, which serves as a superconducting filter of stray magnetic and rf fields.
• The entire probe is placed into a cryostat so that the SQUID, probe, and sample are all at 4.2 K.

2.3.2 Software Improvements

• I have rewritten both the data acquisition and processing software to make it more user friendly with menus and better graphics.
• Also resonance frequencies can be read directly from the screen rather than manually calculated as before.
• The acquisition program also writes the sweep start and stop frequencies, sweep time, and rf strength onto the data file for reference during processing.
• All this improves the data handling aspect of the experiment, but the biggest advances are in the actual control of the spectrometer.
• The overall savings in time and effort for this experiment are significant.

2.3.3 Operation

• Also, the HP sweeper switches synthesizer switches circuits for voltages above 3 volts and this higher voltage circuit is much noisier.
• There is also a two channel mode where two separate frequency sweeps can be initiated simultaneously.
• If the sweeps are over the same region circularly polarized rf can be produced.
• This type of experiment is especially important in the double irradiation scheme presented for 14NNQR (Section 5.3.4).
• This spectrometer allows us to do many NMR and NQR experiments at low frequency and in low field that are normally very difficult to accomplish by other means.

Chapter 3 Z-Axis cw NMR and NQR

• This chapter provides the basic theoretical description of the NMR and NQR techniques utilized in these experiments.
• I will begin by detailing the Hamiltonians that are used to describe the spin system, after which there will be a section on relaxation phenomena.
• The third part of the chapter will describe z-axis cw NMR and NQR detection.
• And, finally, there is a short discussion of experimental lineshapes and intensities.

3.1 Hamiltonians

• Several Hamiltonians describe the basic interactions studied in NMR and NQR experiments.
• The first is the quadrupolar Hamiltonian which arises from the electrostatic interaction between an electric field gradient and the electric quadrupole moment of a nucleus.
• Such nuclei are non-spherical in shape and have a spin, I, greater than 1/2.
• Thus the Zeeman interaction is also present in their NQR experiments, although it is typically only a small but, as the authors will see, necessary perturbation of the quadrupolar Hamiltonian.
• Two other Hamiltonians are also required to describe the experimental situation: the dipole-dipole Hamiltonian, which represents the interaction between the magnetic moments of neighboring nuclei, and the rf field Hamiltonian which characterizes the excitation of the.

3.1.1 The Quadrupolar Hamiltonian

• The quadrupolar Hamiltonian arises from the interaction between the electric quadrupole moment of a nonspherical nucleus (one with I> 1/2) and the surrounding electric field gradient as shown in Figure 3 .1.1.
• The two quadrupolar parameters provide information about the surroundings of the nucleus.
• From the magnitudes of these two parameters one can obtain information such as the symmetry around the nucleus, the size of the deviation from a specified lattice symmetry, paramagnetism (paramagnetic atoms usually have a much larger CQ), coordination number, the effect of impurities and lattice defects, and the distribution of sites in an amorphous material.the authors.

3.1.4 rf Irradiation

• Rf irradiation provides the means for the detection of NMR and NQR signals.
• As rf is swept through resonance, the irradiation causes spins to be excited from the more populated to the less populated state thereby inducing a change in the net magnetization of the sample.
• Iy sin(cot)) 3.10 where the sign of Iy determines the direction (right or left) of circular polarization.

3.2.1 Spin-lattice Relaxation

• Relaxation between the spins and the lattice returns the entire spin system to the lattice equilibrium temperature, the typical starting point for magnetic resonance experiments.
• T 1 determines how often the resonance can be swept for the spins must relax back to equilibrium in order to obtain the maximum signal intensity.
• Among these are organic molecules with methyl groups.
• Also, all the borate glasses the authors have examined have had short Tl'S.
• Thus despite the limitations there are still many interesting samples to be investigated.

3.2.2 Spin-spin Relaxation (Cross-relaxation)

• Spin-spin relaxation is the process whereby the spins exchange energy amongst themselves.
• 59' 60 Crossrelaxation takes place between two levels that are close to or exactly in resonance with each other.
• The dipole-dipole interaction facilitates this transfer in polarization.
• 58 This type of cross-relaxation is important for NQR of half odd integer spin nuclei.
• This solution, however, is limited for powder samples, because the signal intensity will be spread over the entire region from OQ-coz to _Q + t0 z.

3.3.1 Single Crystal NMR (I=1/2)

• To describe z-axis cw NMR, I begin with the simplest case, that of a single crystal with isolated (no dipolar coupling) spin-1/2 nuclei in a magnetic field.
• The populations of the two levels, using the high temperature approximation, are Equilibrium Populations between the dipolar split states.
• This is one of the primary reasons why it is necessary to combine equal numbers of sweeps in different directions (high to low frequency and low to high frequency) in order to avoid biasing the spectrum and the resulting experimental resonance frequency by the direction of the sweep.

3.3.3. Integer Spin NQR

• There is a very fundamental problem when one is working with integer spin nuclei.
• Nondegenerate quadrupole levels have no longitudinal magnetization in zero field.
• When r I = 0 the I+1) levels are degenerate and split from the 10) level by the quadrupolar coupling constant.
• This is similar to the previous case and the authors can use a magnetic field to split the levels and obtain the quadrupolar information.
• 0 then the two levels split into what the authors call the Ix) and ly) states, also known as However when 1"1 _.

3.3.4 Powder Samples

• As usual the situation becomes more complex when powder or amorphous materials are used instead of single crystal samples.
• Thus different crystallites in the sample will have different resonance frequencies depending on their orientation.
• Also, as the pickup coil and rf coils are aligned in the laboratory frame (as is the magnetic field) they are less effective in detecting or irradiating quadrupolar nuclei not aligned with the magnetic field.
• The authors must therefore be satisfied with powders and seek to increase the signal to noise ratio to compensate for the loss in intensity.

3.4 Experimental Lineshapes and Intensities

• Several experimental parameters affect the lineshapes of the observed resonances.
• Figure 3 .12 shows simulated lineshapes for NMR experiments.
• It is diminished because both rf absorption and relaxation are now directly competing at approximately the same rate and it becomes harder to saturate the transition.
• The ideal sweep parameters are a balance between all of these effects.
• 71 I will present data from the SQUID spectrometer that suggest the important potential it has for the study of both binary borate glasses and the measurement of spin-3/2 quadrupolar parameters by means of NQR in a small magnetic field.

4.1.1 Sodium Borate Glass

• Sodium borate glasses can be made by heating NaOH and H3BO 3 to the melting point and then rapidly quenching the mixture.
• To continue this study the authors obtained quadrupolar spectra of the ternary glass system, xNa20.ySiO2.B203.
• According to Bray, there should be many different types of borate structures,67, 72-75but the authors observed only one resonance in each case.
• This could very well be due to extensive overlapping among the lines so they could not be separately resolved.
• A potential solution to this problem is 10B (I=3) NQR, which contains many more lines per site.

4.2 Sodium-23 (I = 3/2)

• Most of these materials, however, have symmetry that preclude the quadrupole interaction, such as the cubic lattice of NaCI.
• From single crystal NMR studies it is found that 11= 0.
• To test their hypothesis, I measured the quadrupolar resonances at different field strengths.
• Attempts were made to study other vanadium compounds, most notably vanadium oxide as a catalyst on a silica surface.
• Also, V205 has a very small quadrupolar coupling constant and so the transitions may have been to low in frequency for detection.

4.5 Manganese-55 (I = 5/2)

• Another transition metal nucleus which I have studied is 55Mn.
• The only nonparamagnetic oxidation state of this element is Mn(VII) which forms the basis for the permanganates, XMnO 4.
• One problem with these samples is their light sensitivity.
• So care was taken to recrystallize the materials and then avoid as much exposure to light as possible.

4.5.1 Potassium Permanganate

• The first sample is KMnO 4, the most common of the permanganate family.
• The one area of agreement for both sets of data is the value of 11.
• Thus the electric field gradient arises primarily from the electric charges of the ions in the orthorhombic crystal structure.
• This leads to the high degree of symmetry evidenced by 1"1 ---0.

4.5.2 Silver Permanganate

• Perhaps a comparison of quadrupolar parameters with the ionicity of the cation-MnO 4-bond should be investigated.
• Also, information about the effect of crystal structure changes and deviations in basic units such as MnO4 could be gained.

Chapter 5 NQR of Nitrogen-14 (I-1)

• Only under unusual circumstances can these resonances be directly detected.
• I will begin this chapter with a detailed explanation of the problem in detection of integer spin NQR.
• Then I will present some data on solid o_-N2 which has been directly detected and illustrates the special case where 11is close to 0.
• Following that I will introduce the indirect method of detection which involves level matching between a proton NMR transition and a nitrogen NQR resonance.
• Finally, I will describe some samples that the authors have studied, among which are amino acids and small peptides, to demonstrate the method and show what information they can learn.

5.1 The Integer Spin Problem

• Integer spin systems present a problem because all nondegenerate states of the system have a vanishing magnetic moment in zero magnetic field.
• The vanishing magnetic moment can be derived in two distinct but equivalent ways.
• First, the brute force method requires the calculation of eigenvalues and eigenstates from the quadrupolar Hamiltonian; e2qQ [312z -12+ 1"1 (12++I2)].

5.2 Direct Detection

• The authors could, however, apply a magnetic field to break the time reversal symmetry and thereby obtain a magnetic moment.
• To calculate this magnetic moment the authors will assume the most favorable of conditions, a single crystal sample with the magnetic field aligned along the quadrupolar z axis.

5.2showsa plot ofF(f) fortypical values ofourNQR experiments.

• From this diagram it is easily seen the magnetic moment is nearly zero unless TI= O.
• One could increase the field, but for powder samples this would mean spreading the signal over a larger frequency range making the corresponding signal intensity smaller.
• So the authors arrive at the conclusion that direct detection of 14N NQR by the SQUID is limited to samples with 11= 0. Here the magnetic field serves to split the I+1) and I-1) states, analogous to the ease of the half odd integer spins (see section 3.3.2).

5.2.1 Solid ¢x-N2

• The authors have been able to directly detect integer spin NQR in one sample, solid a-N 2.
• This width comes from two sources; 1) the splitting due to the magnetic field, which is TB0, and 2) the splitting between states due to TI,which is _h 11.

5.3 Indirect Detection

• It should be noted that the detection of 14N NQR through standard means is not typically inhibited by the vanishing magnetic moment but rather by the low frequency of 14N transitions (typically < 5 MHz), so indirect methods must also be used.
• In the final phase, the proton magnetization is measured at high field.
• Many such cycles must be carried out in order to obtain a single N-14 NQR spectrum.
• The authors technique does essentially the same thing, but no longer involves any field cycling.
• Through cross-relaxation between the nitrogen and nearby protons, mediated by the heteronuclear dipole-dipole interaction, the protons are correspondingly warmed or cooled to finally achieve an equilibrium spin temperature for the level matching states.

5.3.1 Single Sweep

• I will begin by describing the simplest of the level matching methods, the single sweep experiment.
• A spin temperature can be mathematicallydefined for any two level in the following way,58 PI _ exp(-bY-12).

5.3.2 Single Sweep (Vcr _--" 2V h)

• If, instead of the nitrogen level matching resonance equaling vh, it matches 2v h the following adjustments must be made to the derivation.
• Because absolute intensity measurements are not very accurate with the SQUID system this slight increase has not been observed.
• It should also be noted that the tran,,ition matrix elements for this experiment should be smaller than in the previous ease because higher order terms in the dipolar interaction would be needed, namely those involving 3 spins: 2 protons and 1 nitrogen.
• Thus the actual final intensifies may be reduced.

5.3.3 Double Sweep

• The next two methods are attempts to increase the signal intensity by also irradiating the third transition in the nitrogen spin system.
• These experiments are meant to accomplish two objectives.
• Because intensity is proportional to frequency, the v0 line usually is very weak due to its low frequency (typically 100 -600 kHz) as confirmed in The second goal is to connect transitions that are from the same nitrogen site.
• This is easily done if the intensity of the signals can be selectively modified.
• A comparison of these intensities with those from the original method is shown by the dotted lines in Figure 5 .9.

5.3.4 Double Irradiation

• When two transition frequencies have been elucidated then another type of experiment can be done, namely double irradiation.
• This method enhances the intensity of any resonance and so can be used to detect difficult to find transitions (usually v0 because of its low frequency and therefore low intensity) and also to connect transitions when more then one nitrogen site is present in the material.

6.2 Experimental Results

• In this section i present the results that the authors have obtained from the SQUID spectrometer.
• The authors studied a series of straight chained carboxylic acids with 3-15 carbon atoms.
• All of these samples have barriers of the same order of magnitude, however trends due to the functionality at the end of a carbon chain can't be determined because the crystal structures of these molecules are not similar.
• When one looks at other properties of this series such as melting point temperatures and enthalpies of fusion one finds that pentanoic acid is also an extreme.

Full text

LBL-34880
UC-404
II I I I I' I I II
LawrenceBerkeleyLaboratory1
UNIVERSITY OF CALIFORNIA
I II II I I I
Materials Sciences Division
Methyl Quantum Tunneling and Nitrogen-14 _"_ ........, ..
NQR NMR Studies Using a SQUID Magnetic F_._ 2 2 1394
Resonance Spectrometer
OSTI
B.E. Black
(Ph.D. Thesis)
July 1993
I
Prepared for tile U.S. Department of Energy under Contract Number I)E-AC03-76Sl:00098
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LBL-34880
UC-404
Methyl Quantum Tunneling and Nitrogen-14 NQR NMR Studies Using a
SQUID Magnetic Resonance Spectrometer
Bruce Elmer Black
Department of Chemistry
University of California
and
Materials Sciences Division
Lawrence Berkeley Laboratory
University of California
Berkeley, California 94720
i
July 1993
Thisworkwassupportedby theDirector,OfficeofEnergyResearch,Officeof BasicEnergySciences,
MaterialsSciencesDivision,of theU.S.Departmentof EnergyunderContractNo. DE-AC03-76SF00098.
DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED
f

Methyl Quantum Tunneling and Nitrogen-14 NQR Studies Using A
dc SQUID Magnetic Resonance Spectrometer
Copyright © 1993
by
Bruce Elmer Black

Abstract
Methyl Quantum Tunneling and Nitrogen-14 NQR Studies Using A
dc SQUID Magnetic Resonance Spectrometer
by
Bruce Elmer Black
Doctor of Philosophy in Chemistry
University of Califomia at Berkeley
Professor Alex Pines, Chair
Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR)
techniques have been very successful in obtaining molecular conformation and dynamics
information. Unfortunately, standard NMR and NQR spectrometers are unable to
adequately detect resonances below a few megahertz due to the frequency dependent
sensitivity of their Faraday coil detectors. For this reason a new spectrometer with a de
SQUID (Superconducting Quantum Interference Device) detector, which has no such
frequency dependence, has been developed. Previously, this spectrometer was used to
observe liB and 27A1 NQR resonances. I have increased the scope of this study to include
23Na, 51V, and 55Mn NQR transitions.
Also, I present a technique to observe 14N NQR resonances through cross
relaxation of the nitrogen polarization to adjacent proton spins. When the proton Zeeman
splitting matches one nitrogen quadrupolar transition the remaining two 14N transitions can
be detected by sweeping a saturating rf field through resonance. Additionally,
simultaneous excitation of two nitrogen resonances provides signal enhancement which
helps to connect transitions from the same site. In this way, we have observed nitrogen-14
resonances in several amino acids and polypeptides.
This spectrometer has also been useful in the direct detection of methyl quantum
tunneling splittings at 4.2 K. Tunneling frequencies of a homologous series of carboxylic