Richard Edden

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I was recently asked by a great friend to answer some questions about NMR. "I need NMR for Dummies" was the self-deprecating quote. I have tried to answer in plain language without resorting to maths. Inevitably, some of the detail gets lost, but I think that what remains is a useful start for anyone familiar with NMR, interested in going a little deeper and not interested in wading through the (very rewarding) maths. Being as this is, one side of a conversation, the ordering is jumbled, but three you are...

Apologies to the real "... for Dummies" people, who have an NMR chapter in Organic Chemstry for Dummies. To anyone wanting a better explanation, I would recommend the excellent book Understanding NMR Spectroscopy.

Gradients

A basic NMR experiment is run with the static magnetic field shimmed, so that it is as homogeneous as possible (the same everywhere throughout the sample). During a gradient pulse, the magnetic field is deliberately made inhomogeneous. For example in a z-gradient, the magnetic field at the top of the sample is made slightly stronger than the field at the bottom of the sample. This is achieved by passing a current through a little electromagnet coil which has been specially designed to alter the field in this way.

Why would I want to do this? Any multiple pulse NMR experiment will produce a variety of different signals. Some we want to see and some we don't. For any experiment to give us the information we want, we need to find a way of suppressing the signals we don't want to see (e.g. COSY peaks in a NOESY experiment). There are two main ways of doing that: phase cycling and gradients.

In a phase cycle, we repeat the experiment a number of times, each with the RF pulses set to have a different phase. In the end, the signals are added together so that the unwanted signals subtract away and the desired signals add up and are seen. A gradient experiment achieves the same thing in a single scan.

The basic idea is that in an experiment with gradients in it, the signal evolves differently in different parts of the sample (because the field is different during the gradient pulse). By the end of the experiment, the signals you want have all been refocused so that you get a good strong signal from the sample as a whole. The signals you don't want to see have a different phase in different parts of the sample, and so when you acquire the signal from the sample as a whole, these signals cancel each other out and are removed from the spectrum.

Precession

The simplest NMR experiment (like a 1D proton measurement) consists of a 90 degree pulse and then a period of acquiring data - so called pulse-acquire or 90-acquire experimnets. (One variation on this theme is to not use a 90 degree pulse, but a 30 degree pulse. This is done for reasons of relaxation, which might be a good topic for another email.) Let's consider what happens to the magnetization during this experiment. First, I suppose we should run over what magnetization is, where it comes from and how it behaves.

The nucleus of a hyrdogen atom (and others, 13 C 19 F etc) has a 'spin' associated with it. Essentially that means that the nucleus acts a little like a small magnet. In the presence of a large magnetic field, the magnets can either align with the magnetic field (spin up) or against the magnetic field (spin down). There is a slight energetic advantage to the spins being up, and so out of a large number of spins in an NMR tube, there will be a slightly larger number pointing up than down. The sum of all the individual spins, each behaving a little like a small magnet, gives rise to the 'bulk magnetization', which is best thought of as an arrow pointing UP. It is not too important to understand what that is (other than that it arises as the sum of the magnetizations of each individual spin within the sample), but it is very important to understand how it behaves.

The first important property of the bulk magnetization is that, at equilibrium, it points along the direction of the magnetic field. This equillibrium magnetization is the starting point of any NMR experiment. Once an experiment has been run, relaxation processes allow the equilibrium magnetization to recover to its original position.

The second important property of magnetization is that, if the magnetization is no longer points along the magnetic field, it will PRECESS around it. Precession is like the wobbling of a spinning top; the base of the 'magnetization arrow' stays in the same place, and the tip traces out a circle. In the extreme case that the magnetization has been disturbed from the equilibrium direction (which is assigned as the z-axis) by 90 degrees, the precession of the magnetization occurs in the transverse plane. So the arrow traces out a disc, such that is is always at 90 degrees to the z-axis.

(If this does not make clear sense, a couple of diagrams will help a lot. Either get me to draw them, or look up the Vector Model in one of the NMR books in the lab and it should have diagrams showing this precession behaviour).

So hopefully we have a handle on what precession is. The next question is "When would this happen?" or "how does the equlibrium magnetization ever get disturbed from the z-axis?". And the answer to this is the RF pulse. A pulse is a brief magnetic field that is deliberately applied at an angle to the equilibrium magnetization (e.g along the x-axis). How does the magnetization respond to the new magnetic field? It precesses around it! So a 90-degree is simply a period during which an extra magnetic field is applied along the x-axis, so that the equilibrium magnetisation precesses around it through a quarter of a revolution. The magnetization is then pointing along the y-axis and will continue to precess about the static magnetic field when the pulse is over.

Phase

Next question - "What is phase"? Phase is a concept that pops up all over the place in NMR. It describes direction, in the same way as a compass bearing does ( a bearing of 270 degrees is the same as saying West; a phase of 270 degrees would mean that the ). When magnetization precesses, its PHASE is constantly changing, as if the compass needle is spinning around. So the phase of magnetisation is which direction it points in the x,y plane. Remember, the equilibrium magnetisation points purely in the z-direction, and so has no phase.

Another place that the word phase pops up is as in 'phasing a spectrum'. The need to phase a spectrum arises because we don't know precisely which direction the magnetisation is pointing in when we start to acquire data. We just know we have disturbed the equilibrium magnetisation with our pulse (and therefore the magnetisation is precessing about the z-axis). So when we acquire data, we acquire two sets of data (real and imaginary) that come from two receivers positioned at 90 degrees to one another. Phasing is the process of mixing these two channels of data. If the magnetisation was aligned perfectly with the Real receiver at the time when acquisition starts, then no phasing would be necessary. What I have described here is the zero-order phase correction. The first order correction will come in the next section.

Another place that phase comes up in NMR is to describe the phase of pulses. If our 90 degree RF pulse is applied along the x-axis, the magnetisation ends up along the y-axis at the end of it; conversly if the pulse is applied along the y-axis, the magnetisation ends up along the x-axis at the end of it. The direction along which the pulse (remember a pulse is just a magnetic field that points in a certain direction in the x,y plane and lasts for a short duration) points is its phase. A simple 0 1 2 3 phase cycle (these are written as ph1 = 0 1 2 3 at the bottom of the Bruker pulse programs) meand that the experiment is performes 4 times, once with the excitation pulse along the x-axis (0), once along the y-axis (1), once along the negative x-axis (3) and once along the negative y-axis (4). If we simply added the data from these four experiments up without doing anything else, we would get no data at all. This is because the data from the 0 and 2 experiments will have opposite phase and so cancel each other out to zero, and likewise the 1 and 3 experiments. (Actually the only thing that won't subtract perfectly is the noise, since that is not caused by the experiment itself and just 'happens anyway'.) In order to not lose all our signal, the phase of the receivers also has to change - so the pulse program would have a line in it like ph31 = 0 1 2 3, as well, so that the data from each of the four experiments adds up, rather than subtracting away. What is means to change to phase of the receivers and quite why we would want to do this phase cycle, are things for another day.

A final important thing to say about phase was just demonstrated. If we add up signals with different phases, they will tend to subtract from one another. This is importnat in gradient experiments.

Refocusing

The reason a sample gives us an NMR spectrum is that different spins precess at a different rate, depending on their chemical shift. Imagine a 90-delay-acquire experiment. The equilibrium magnetisation of all spins is disturbed from the z-axis by the RF pulse and at the start of the delay, the phase of all magnetisation is the same. Because different spins then precess at a different rate, the magnetisation splits into different arrows, each one representing a group of spins with the same chemical shift, which each precess during the delay (at the rate corresponding to their chemical shift). If acquisition is started at the end of the delay, the spectrum will be difficult to phase as the different peaks will have a different phase (because of precession during the delay). However, the phase of the peaks can be precisely determined - it just depends on the initial phase of the magnetisation after the RF pulse, the duration of the delay and the chemical shift of the peaks. This is precisely the role of the first-order phase correction, it adds a different phase at different points in the spectrum so as to correct for little delays in the experiment.

Imagine another experiment, which starts 90-delay, as above. At the end of it the magnetisation all has a differnet phase depending on its chemical shift. Now imagine turning back the direction of time, so that all the magnetisaitons precess in the opposite direction. After a certain period, we will get back to the initial situation we were at after the 90 pulse - all the magnetization will have the same phase irrespective of chemical shift. The chemical shift offset is said to be refocused. This is precisely what happens during a spin echo (except the time-reversal bit.).

In a gradient, the rate of precession of magnetisation depends not on the chemcial shift, but on the position in the sample. But the theory is the same. Imagine a 90 pulse followed by a gradient. At the beginning of the gradient all the magnetisation has the same phase. At the end of the gradient, the phase of the magnetisation depends on the position in the sample. If we acquire a spectrum at this point, we will get no spectrum as the different parts of the sample will give signals (with the same chemciacl shift) with different phases, so our signal will subtract from itself and be suppressed. However, all is not lost. We can apply a second gradient with the same size but opposite direction. In this gradient, spins which previously precessed forwards quickly will precess back quickly and those that previously precessed back slowly will precess forward slowly, so that by the end of the second gradient, all the precession has been undone (or REFOCUSED) and the magnetization throughout the sample has the same phase.
















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