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Nuclear magnetic resonance (NMR) spectroscopy is a very powerful tool for the determination of chemical structures of compounds. The technique places nuclei into a powerful magnetic field, , which causes nuclei with a magnetic moment, , to respond by precessing around the vector of the applied magnetic field, predominantly at specific energy levels. The number of these energy levels is determined by the spin quantum number, I, which may take integer and half integer values from zero upwards and can be predicted by the number of protons and neutrons in the nuclei: if the number of protons and the number of neutrons are both even (e.g. 12C), the nucleus has no magnetic moment and I=0. If both numbers are odd (e.g. 2H â‰¡ D), I takes integer values (not including 0), and if there are an odd number of nucleons, I only takes half-integer values ( etc) (e.g. I(1H) = , I(13C) = ). This relationship arises due to the fact that protons, neutrons and electrons each have spin quantum numbers of I = , and nucleons will pair up with their counterparts of anti-parallel spin. The magnetic quantum number, m, has 2I+1 possible values in integer steps between +I and -I.
These small population differences are what the NMR spectrometer detects. However if all the spectrometer detected was the magnetogyric ratio of an element within a known magnetic field, it would only serve to identify the elements contained in a compound. Fortunately, electrons belonging to the nucleus are induced into circulating within their atomic orbitals, inducing their own magnetic field in the opposite direction, shielding the nucleus from a small amount of the magnetic field. Thus a shielding constant (a molecular property), Ïƒ, can be applied to the magnetic field, B, to replace the term with B(1-Ïƒ), which will differ for nuclei in different electronic environments. The resonance frequency of the nucleus becomes: Î½ = Î³B(1-Ïƒ)/2Ï€.
Another effect on the frequency is spin-spin coupling, also known as J-coupling: which causes a chemically shifted peak to split due to antiparallel and parallel nuclear spins of neighbouring nuclei. The energies of these splitting are E = h JAX mA mX, (where JAX is the coupling constant measured in Hz and can be positive or negative depending on whether parallel or antiparallel spins are energetically favoured) for any interacting nuclei A and X, which inserted into the equation above, means that:
For multiple coupling interactions, multiple splitting will occur, and splitting of the same energy will provide a ratio of peak intensities correlating to Pascal's triangle.
Since these frequencies are specific to a given spectrometer (due to the spectrometer's magnetic field), it is customary to define this frequency difference, or "chemical shift" in terms of a reference frequency Î½ref, to give a molecular property, Î´, unrelated to the spectrometer measuring it. i.e.: Î´ = (Î½ - Î½ref)/Î½ref (usually quoted in ppm or "parts per million").
Bloch Spheres and the Carr-Purcell Spin-Echo Pulse Sequence
As we have seen, the nuclei rotate at the order of 108 Hz in the laboratory reference, which is very difficult to visualise, especially when considering how pulse sequences affect these spins. It is therefore helpful to view the nuclear spin state in a rotating frame of reference, as seen, where the observer is rotating at the Larmor frequency with the nucleus. It is important to note here, that although the Bloch sphere shows a single vector representation of the spin states in a sample, it is actually a resultant of all of the precessing spin states in the sample that is detected.
The Carr-Purcell spin-echo pulse sequence involves a 90Â° pulse about the x-axis, followed by a time Ï„, a 180Â° pulse about the y-axis and another delay of time Ï„, before collecting the Free Induction Decay (FID) i.e. [90Â°X - Ï„ - 180Â°Y - Ï„ - FID]. This sequence is displayed as a pulse sequence and as a Bloch sphere representation below:
As can be seen in (Fig 3a), immediately after the 90Â°X pulse, a coherent magnetisation of the nuclei is produced, which can be measured as the FID, before the variation in precessional speeds desynchronises it to produce a net magnetisation of zero. However, by application of a 180Â°Y pulse, spins will be returned at the same precessional frequency, and thus after the same time, will resynchronise to reproduce the coherent magnetisation, which is then collected as the FID.
Diffusion-Ordered Spectroscopy (DOSY) (4 page target)
DOSY [1,2] spectra add a dimension to traditional 1D and 2D spectra, in order to provide a measurement of the diffusion coefficient, creating 2D[1,2,3] and 3D[2,4,5] spectra respectively. It is thus possible to resolve a mixture of chemicals with different diffusion coefficients, even when a traditional 1H spectrum, for example, may not distinguish between two overlapping peaks.
There are many pulse sequences with which one can run a DOSY spectrum.[1,2] These ideally require the use of pulsed field gradients (G), discussed below, in addition to the usual radiofrequency pulses (RF).
The basic DOSY sequence, PFGSTE (Pulsed Field Gradient STimulated Echo), essentially a variant of the Carr-Purcell spin-echo pulse sequence which applies pulse field gradients, is shown below:
Since the second 90Â° pulse in the above sequence moves the magnetisation back into the axial region after applying the pulsed field gradient, the J modulation and spin-spin (T2) relaxation that would normally evolve during transverse magnetisation in homonuclear systems is limited.
J modulation results from hard radiofrequency pulses exchanging the spin states of coupling nuclei being observed, preventing complete refocusing, and thus distorting the signal. Thus the sensitivity cost of only half of the net initial transverse magnetisation refocusing is worth the removal of J coupling from the results. Therefore, for more selectivity, the Oneshot pulse sequence is used for the remainder of this project to collect DOSY data:
Pulsed Field Gradients
Pulsed field gradients are integral to understanding a DOSY pulse sequence. These are pulses of linear variations in the magnetic field across the length of the sample, which thus alter the nuclear frequency of precession depending on the nucleus' location within the sample, allowing positional information to be encoded into the outputted spectra. This has the basic effect of "winding up" the nuclei in a helical pattern, based on their positions within the sample.
Multiple FIDs are recorded with different gradients, and peak intensities in successive spectra are used in conjunction with the Stejskal-Tanner equation below to calculate the diffusion coefficient, which is then plotted against the desired spectrum on a 2 dimensional plot.
Where S is the signal amplitude at gradient G, S0 is the signal amplitude in the absence of diffusion, D is the diffusion coefficient, Î³ is the magnetogyric ratio, G is the gradient amplitude, Î´ is the gradient pulse width and Î”' is the diffusion time corrected for diffusion during finite gradient pulse widths. For the DOSY Oneshot sequence, the diffusion delay Î” is defined as the period of time between the midpoints of each pair of gradient pulses as shown in the sequence, and the diffusion time correction is -Î´/3. The sequence can thus be adapted to produce:
A series of pulse field gradient stimulated echo spectra is recorded with increasing pulsed field gradient field strengths, and the resulting signal decay is fitted to this Stejskal-Tanner equation, where the magnetogyric ratio Î³ , pulsed field gradient amplitude G and duration Î´, and the diffusion delay Î” are known, and where D the diffusion coefficient is calculated.
The crucial part of the DOSY method is that during the diffusion delay Î”, molecules diffuse, and when the second set of selection gradient pulses are applied to "unwind" the nuclei, those that have changed position are not fully unwound, and thus do not contribute to the spin echo as fully either, resulting in a lower refocusing of signal. For stronger gradients, this is more noticeable, since the molecules remain more out of phase, and thus contribute less. Thus repeating a DOSY scan at increasing gradient strengths should result in signal decay.
Pure Shift (4 page target)
The biggest problem with NMR spectroscopy is the complexity of interpretation of the resultant spectra, hence the continued development of more powerful magnetic fields to increase resolution and 2D methods to discover which nuclei are coupled together. Another method of simplifying spectra is by effectively removing the J-coupling, in order to create spectra which are based on the pure chemical shift of nuclei alone, giving rise to its name. This method essentially replaces multiplets in spectra with singlets, which often makes the origins of complicated overlapping regions of spectra much easier to identify.
However no coupling information is necessarily lost, since an optional extra dimension can be recorded without pure-shifting, in order to retain the J coupling data.
The pulse sequence for pure shift spectroscopy uses gradients during pulses to select a frequency range of a spectrum, which it then records its FID for 10-20 ms, in order to ensure that its duration is shorter than the time in which scalar couplings can evolve. The recorded FIDs from each frequency range are then "stitched" together to produce a resultant FID which is equivalent to one over the whole frequency range of recorded spectra. This method was first suggested by Zangger and Sterk in a paper demonstrating a 1D proton-decoupled 1H spectrum and an Ï‰1-decoupled TOCSY spectrum (i.e. decoupled in one frequency dimension), the latter of which has recently been repeated, but decoupled in both dimensions.
The slice selection gradients are used to break a sample into slices, and shift spectra in each increment based on the magnetic field it experiences. A selective pulse is then used to select a specific frequency range from each of these slices' spectra and record them in one spectrum for the whole sample, while all other frequencies are inverted by a 180Â° pulse, refocusing them along with their J couplings, thus eliminating them from the spectra.
Pure Shift DOSY (4 page target)
This combination of DOSY with pure shift techniques attempts to produce 2D spectra of singlets showing diffusion coefficients along the second axis.
The pulse sequence is essentially an amalgamation of the DOSY pulse sequence with the pure shift sequence: the DOSY sequence ends with the FID it wishes measured at the end of its section - the pure shift addendum therefore does not require its initial 90Â° pulse, but instead only to selectively refine the DOSY FID to be interpreted as a DOSY pure shift FID.
The overall sequence is shown below illustrating the breakdown between the DOSY sequence and the pure shift selection sequence:
Problems combining Pure Shift with DOSY
The main issue with combining the above sequences is that the resultant spectra, once pure-shift-processed and the DOSY processed, show a curvature of the diffusion coefficient, which is clearly not feasible: a difference in magnitude of the magnetic field experienced by each molecule will not lead to a decrease in the diffusion coefficient.
For each slice of sample measured by the pure shift method, the signal attenuation measured by the DOSY can be modelled by the Stejskal-Tanner equation, because the gradient strength at each slice determines the diffusional attenuation for its corresponding chemical shift.
This problem arises because the gradient is weaker at the edges of the measured sample, and thus, since attenuations of the signals in DOSY spectra are measured as a function of the gradient strength, as explained in the DOSY section, the regions at the edges of the sample show least attenuation.
This correction for the pure-shift-altered diffusion coefficient used in DOSY is what this project intends to accomplish.
The ratio of apparent diffusion coefficient will be compared with the measured diffusion coefficient, and a polynomial fitted to this, in order to correct a varying pure shift DOSY diffusion coefficient to a constant diffusion coefficient measured by a simple set of DOSY spectra.
This will further enable variables (such as the maximum gradient strength G, and its positional variation and centring, both with frequency and in the measured sample volume) to be integrated into the polynomial, to allow this correction to be more widely applied to multiple spectrometers.
Ideally, the method will allow a calibration sample to be analysed and a NUG to be corrected for by weighting the correction algorithm appropriately.
The resulting correction and method for its calibration will then be added to the DOSY Toolbox.
The DOSY Toolbox
The DOSY Toolbox is intended as a free complementary software suite to process DOSY data with a variety of methods available to accomplish this. Since most DOSY processing methods assess attenuation of the amplitude of peaks within the spectra, it is often necessary to correct for any noise within the spectra.
Interpreting DOSY data
The DOSY Toolbox is controlled by a graphical user interface (GUI). This contains a window for time and frequency domain spectra to be displayed (as FID and traditional NMR spectra, respectively), including the effect of Gaussian and Lorentzian weighting of either of these domains. Underneath this window lies a variety of tools to aid in the removal of unwanted noise from raw DOSY spectra, including phase correction, baseline correction (to correct for curvature) and reference deconvolution (by use of FIDDLE). Non Uniform field Gradients (NUGs) can also be taken into account during processing of refined DOSY data, rather than using simple exponential fittings.
HR-DOSY[2,3] - a uni-variant method - and DECRA, MCR, SCORE & PARAFAC - multi-exponential methods - are tools included in this software to further analyse acquired data.
In this project, HR-DOSY is primarily considered: a series of scans at differing gradient strengths is recorded and a plot of signal intensity against gradient strength is plotted (hence the importance of a high signal to noise ratio - otherwise signal intensity will not be representative of the resultant echo).