The theoretical background for these experiments and the spin dynamics of the interferometry are also discussed. EXPERIMENTAL DETERMINATION OF THE 13 c CHEMICAL SHIFT SENSOR IN K2Pt(CN) 4Br0_3·3H20 USING HETERONUCLEAR DIPOLAR EN. The second part of the thesis, chapters 5-8, deals with a technique called dipolar modulation chemical shift spectroscopy.
CHAPTER 2
BASIC THEORY FOR THE
PHASE INTERFEROMETRIC EXPERIMENTS
INTRODUCTION
We assume the following initial conditions. which means that at timet= 0 our system is in state ~1•. 2. Furthermore, there is a clear phase coherence between these states, and we have chosen the difference in the phases of the two complex amplitudes to be zero. In the experiments of chapters 3 and 4 this operator is the transverse magnetization; however, in the most general case, any such "off-diagonal" operator could be suitable.
CHAPTER 3
EXPLICIT DEMONSTRATION OF SPINOR CHARACTER FOR A SPIN ~ NUCLEUS
USING NUCLEAR MAGNETIC DOUBLE RESONANCE PHASE INTERFEROMETRY
Vaughan, entitled "Explicit Demonstration of Spinor Character for a
We can see that applying a selective 2n pulse to only one of the. The presence of spin~ would split this resonance line into a doublet and a spin!;. The letters a and 8 represent the two eigenstates of the up and down spin of the ~ particle.
CHAPTER 4
NUCLEAR MAGNETIC DOUBLE RESONANCE PHASE INTERFEROMETRY
- DESCRIPTION AND EXPLANATION OF THE EXPERIMENT A. General Description
- PRESENTATION AND DISCUSSION OF RESULTS A. Relaxation Data
By solving these equations we can determine the relevant matrix elements at the end of the 13c pulse of length. As in the other cases, equations (13) for the evolution of the density matrix after the 13c pulse still apply. After examining equations (31), we see that the effects of the relaxation are threefold.
CHAPTER 5
BASIC THEORY FOR THE EXPERIMENTS UTILIZING DIPOLAR OSCILLATIONS
CHAPTER 6
In particular, both the pulse version of the original Hartmann-4ahn experiment and the multiple pulse sequence used to demonstrate simultaneous polarization transfer and homonuclear dipolar suppression are shown. Extending the use of multiple pulse techniques into this domain provides greater flexibility for designing double resonance experiments to provide electronic, structural, and dynamical information. While large-scale dipolar oscillations are not expected in 8PbF2 due to indirect Pb-F-Pb interactions, the results of suppression of homonuclear dipolar interactions are evident in these spectra.
This four-pulse cycle consisted of applying 90°x pulses coinciding with each x pulse of the eight-pulse cycle, and 90°_x pulses coinciding with the -x pulses (all orientation information (x ,y,z) refers to directions in the appropriate rotating reference frame). The transverse components of the magnetization parallel to the x-axis in both I- and S-spin systems are observed at the end of successive cycles and illustrated in Figure 1A. An analysis of this data is used to provide an accurate characterization of the transfer process (9). Note that while the oscillatory curve observed for the I-spin.
Figures 1B and 1C allow a comparison of the "sharpness" of the double resonance condition with and without suppression of the homonuclear dipolar coupling. The behavior of the S spin polarization under different mismatch conditions is illustrated and shows the "diffusivity" of the double resonance measure in this pulse analogue of the Hartmann-Hahn experiment (1). It should be noted that an order of magnitude smaller mismatch of the double resonance condition is required in the case of dipolar suppression, to disrupt polarization transfer.
The magnitude of the observed magnetization in the x direction of the respective rotating frames is plotted on the ordinate, with one unit representing the thermal equilibrium polarization at room temperature.
CHAPTER 7
HETERONUCLEAR DIPOLAR MODULATED CHEMICAL SHIFT SPECTRA
PART ONE
In the first, preparatory period, a transverse magnetization for the S (dilute) spin species is produced and any net magnetization in the spin system is destroyed (the destruction of the I spin magnetization is not theoretically necessary, but is an experimental precaution). In the second period, an evolution of the 1-S heteronuclear dipolar Hamiltonian is allowed to take place for a period <, while simultaneously suppressing the abundant spin-dipole-dipole interaction with an eight-pulse sequence {G). This provides a convenient way to experimentally determine the numerical values for a by observing spectra of the I-spin system as a function of the frequency offset, t.
The next step within this evolutionary period is to reorient the time evolution of the off-resonance and chemical shift Hamiltonians in the S-spin system by applying a 180° pulse to the S-spin system, causing the production of a spin echo arises at a certain point in time. later time point (the phase of the 180° pulse was chosen parallel to the initial cross-polarizing field to obtain a Carr-Purcell-Meilboom-Gill type echo). When the time decay of the magnetization is Fourier transformed, powder patterns are obtained that contain the heteronuclear dipolar evolution as a modulation. By collecting spectra for different values of the time, T, of the dipolar evolution, detailed geometric information can be obtained.
This includes orientation of the 1-S vector in the chemical shift principal axis system and a determination of the I-S vector length and, as illustrated in some of the data presented here, information about the motion of the 1-S vector in the laboratory frame . To observe what effect such molecular motion can have, theoretical spectra were calculated using the fitted values of the chemical shift tensor and a broadening function from the conventional powder pattern (T = 0). The height or value along the f-axis corresponds to the expected intensity for a given value of the length of the dipolar evolution period, T, at a particular resonance frequency, w, in the adsorption spectrum.
The experimental and theoretical spectra were normalized only to T = 0, and quantitative comparisons can be made between the theoretical and theoretical spectra.
PART TWO
CHAPTER 8
Some of the material in Chapter 8 is taken from an article by M. E. Stoll, A. J. Vega, and R. W. Vaughan, entitled "Structural Information in Polycrystalline Systems Via Dipolar Modulated Chemical Shift. The rest of the material in Chapter 8 is taken from an article that is This experiment is the homonuclear analog of the heteronuclear dipolar modulated chemical shift experiment in Chapter 7, and thus the motivation is also analogous.
To achieve this goal, we use the orientation-dependent dipolar interaction to modulate the conventional high-resolution po1 chemical shift model. From computer simulations of the spectra for various parameters, we are able to determine the length of the proton-proton bond and its orientation with respect to the chemical shift reference frame of the major axis. The spin dynamics of the corresponding mean Hamiltonian was discussed in Chapter 5, in the section dealing with the homonuclear dipolar Hamiltonian.
The high degree of isolation of the I-I pairs ensures that the normal polycrystalline proton NMR powder pattern will also be rich in detail. From symmetry we know that the chemical shift tensors of the two protons (see Figure 1) are identical and that these protons have the same local value. We believe that these results confirm the validity of the homonuclear dipolar modulated chemical shift technique.
Using the dipolar modulated experiments, we can determine from a powder some information about the relationship between the molecular framework and it.
CHAPTER 9
HETERONUCLEAR DIPOLAR AND QUADRUPOLAR INTERACTIONS
The results reported here provide information on the anisotropy in the electronic structure of cyanide in this square planar platinum complex and can be compared, for example, with measurements of the chemical shift tensor of 13 C. Crystal orientations were determined from the anisotropic optical properties of the crystal together with NMR spectra. Due to the high degree of symmetry at each carbon site, the orientation of the principal axis of the chemical shift tensor (7) can be determined, as shown in Figure 1.
N energy levels as a function of the angle, n, between the direction of the magnetic field and the axis of symmetry of the electric field gradient. This accounts for the gross difference between the two solutions shown in Figure 2b and illustrates how the presence of the nitrogen quadrupolar interaction produces large qualitative effects in the 13 C spectra. 11• In all cases good qualitative agreement was obtained between the experimental and the calculated, thus providing a strong rationale for the validity of the analysis presented here.
The asymmetric nature of the spectra generated by the presence of the 14 N quadrupolar interaction is. Thus, the effect of the cyanide bond to the platinum, and any associated effects due to the particular solid state structure, primarily affect the carbon chemical shift tensor by producing a non-zero (0.2) asymmetry about the C–N bond. The principal axes of one of the carbon atoms are illustrated, as is the nomenclature (6 and.
The dipolar splitting of carbon from nitrogen is shown as a function of n (note that the axis of symmetry of the nitrogen quadrupole interaction is assumed to be parallel to the C-N internuclear vector).
APPENDIX
A SIMPLE SINGLE-COIL NUCLEAR MAGNETIC DOUBLE RESONANCE PROBE FOR SOLID STATE STUDIES
This scheme has been used over the past two years on a variety of frequencies, and the detailed discussion of the. These equations are obtained from an essentially zero order approximation which involves ignoring small residual effects of c1 and c2 on the high frequency response and of c. 3 and c4 on the low-frequency response of the probe. This version of the probe is designed for operation within a 4.8 em wide gap of a conventional electromagnet, and consequently no serious space problems.
Due to the inherent difficulties of working with the high RF frequency used in this version (270 MHz), special attention had to be paid to the physical construction of the probe and its components to avoid additional and unwanted inductances and capacitances. 40 pf, and since the outer cylinder is grounded, it forms the bulk of the matching capacitor, c4. 3 part of the cylindrical unit shown in Figure 2 was used with additional fixed ceramic (2S) capacitors in parallel to give a total capacitance of 32 pf.
The Q of the 67.9 MHz portion was measured near 80, and no measurable power loss could be attributed to the A/4 cable at this frequency. The use of both commercial filters was necessary in this case in order to: (a) protect the receiver from overloading due to the high-power rf signal at the second frequency and (b) prevent the power input signal from high to contain any rf component at the detection frequency (once such a signal reached the probe, it could not be removed by any filtering without also filtering the NMR signal to be observed). An example of probe performance in this second mode is illustrated in Figure 3, which is an oscilloscope snapshot of the 207Pb NMR signal observed in PbF.
Comparison of the two traces shows no observable increase in the noise level of the 12.5 MHz channel (207Pb) when high power is applied to the 56.4 MHz channel (19F).
PROBE
