1
Getting Started

1.1 The Technique

This book is not really intended to give an in-depth education on all aspects of the NMR effect (there are numerous excellent texts if you want more information), but we will try to deal with some of the more pertinent ones.

The first thing to understand about NMR is just how insensitive it is compared with many other analytical techniques. This is because of the origin of the NMR signal itself.

The NMR signal arises from a quantum mechanical property of nuclei called 'spin'. In the text here, we will use the example of the hydrogen nucleus (proton) as this is the nucleus that we will be dealing with mostly. Protons have a 'Spin Quantum Number' of ½. In this case, when they are placed in a magnetic field there are two possible spin states that the nucleus can adopt and there is an energy difference between them (Figure 1.1).

Figure 1.1 Energy levels of spin ½ nucleus.

The energy difference between these levels is very small, which means that the population difference is also small. The NMR signal arises from this population difference and hence the signal is also very small. There are several factors which influence the population difference and these include the nature of the nucleus (its 'Gyromagnetic ratio') and the strength of the magnetic field that they are placed in. The equation that relates these factors (and almost the only one in this book) is shown here:

? = Energy
? =Gyromagnetic ratio
h =Planck's constant
? =Magnetic field strength

Because the sensitivity of the technique goes up with magnetic field, there has been a drive to increase the strength of the magnets to improve sensitivity.

Unfortunately, this improvement has been linear since the first NMR magnets (with a few kinks here and there). This means that in percentage terms, the benefits have become smaller as development has continued. But sensitivity has not been the only factor driving the search for more powerful magnets. You also benefit from stretching your spectrum and reducing overlap of signals when you go to higher fields. Also, when you examine all the factors involved in signal to noise, the dependence on field is to the power of 3/2 so we actually gain more signal than a linear relationship. Even so, moving from 800 to 900 MHz only gets you a 10% increase in signal to noise whereas the cost difference is considerably more than that!

In order to get a signal from a nucleus, we have to change the populations of each spin state. We do this by using tuned radio frequency to excite the nuclei into their higher energy state. We can then either monitor the absorption of the energy that we are putting in or monitor the energy coming out when nuclei return to their low energy state.

The strength of the NMR magnet is normally described by the frequency at which protons resonate in it - the more powerful the magnet, the higher the frequency. The earliest commercial NMR instruments operated at 40 megahertz (MHz) (megacycles in those days) whereas modern NMR magnets are typically ten times as powerful and the most potent (and expensive!) machines available can operate at fields of over 1 GHz.

1.2 Instrumentation

So far, we have shown where the signal comes from, but how do we measure it? There are two main technologies: Continuous Wave (CW) and Pulsed Fourier Transform (FT). CW is the technology used in older systems and is becoming hard to find these days (we only include it for the sake of historical context and because it is perhaps the easier technology to understand). FT systems offer many advantages over CW and they are used for almost all modern instruments.

1.2.1 CW Systems

These systems work by placing a sample between the pole pieces of a magnet (electromagnet or permanent), surrounded by a coil of wire. Frequency-swept radio frequency (RF) is fed into the wire, or alternatively, the magnet may have extra coils built onto the pole pieces which can be used to sweep the field with a fixed frequency. When the combination of field and frequency match the resonant frequency of a nucleus, radiofrequency is absorbed by the nuclei and re-emitted and captured by a receiver coil perpendicular to the transmitter coil (Figure 1.2). This emission intensity is then plotted against frequency. The whole process of acquiring a spectrum using a CW instrument takes typically about 5 minutes. Each signal is brought to resonance sequentially and the process cannot be rushed!

Figure 1.2 Schematic of a CW NMR spectrometer.

1.2.2 FT Systems

Most spectrometers used for the work we do today are Fourier transform (FT) systems. More correctly, they are pulsed Fourier transform systems. Unlike CW systems, the sample is exposed to a powerful polychromatic pulse of radio frequency. This pulse is very short and so contains a spread of frequencies (this is basic Fourier theory and is covered in Chapter 2). The result is that all of the signals of interest are excited simultaneously (unlike CW where they are excited sequentially) and we can acquire the whole spectrum in one go. This gives us an advantage (known as the Felgett advantage) in that we can acquire a spectrum in a few seconds as opposed to several minutes with a CW instrument. Also, because we are storing all this data in a computer, we can perform the same experiment on the sample repeatedly and add the results together. The number of experiments is called the number of scans (or transients, depending on your spectrometer vendor). Because the signal is coherent and the noise is random, we improve our signal to noise with each transient that we add. Unfortunately, this is not a linear improvement because the noise also builds up albeit at a slower rate (due to its lack of coherence). The real signal to noise increase is proportional to the square root of the number of scans (more on this later).

So if the whole spectrum is acquired in one go, why can't we pulse really quickly and get thousands of transients? The answer is that we have to wait for the nuclei to lose their energy to the surroundings. This takes a finite time and for most protons is just a few seconds (under the conditions that we acquire the data). So, in reality we can acquire a new transient every 3 or 4 seconds.

After the pulse, we wait for a short while (typically a few microseconds), to let that powerful pulse ebb away, and then start to acquire the radio frequency signals emitted from the sample. This exhibits itself as a number of decaying cosine waves. We term this pattern the 'free induction decay' or FID (Figure 1.3).

Figure 1.3 A free induction decay (FID).

Obviously this is a little difficult to interpret, although with experience you can train yourself to extract all the frequencies by eye. (only kidding!). The FID is a 'time-domain' display but what humans really need is a 'frequency-domain' display (with peaks rather than cosines). To bring about this magic, we make use of the work of Jean Baptiste Fourier (1768-1830) who was able to relate time-domain to frequency-domain data. These days, there are super-fast algorithms (the Cooley-Tukey algorithm, for example) to do this and it all happens at the press of a button. It is worth knowing a little about this relationship as we will see later when we discuss some of the tricks that can be used to extract more information from the spectrum.

There are many other advantages with pulsed FT systems in that we can create trains of pulses to make the nuclei perform 'dances' which allow them to reveal more information about their environment. Ray Freeman coined the rather nice term 'Spin Choreography' to describe the design of pulse sequences. If you were fortunate enough to be able to attend one of his lectures, Ray Freeman had the gift of making this complex, mathematical subject easy to understand. Ray's NMR textbooks are a great source of information if you want to understand more. In particular, his book, Spin Choreography Basic Steps in High Resolution NMR (Oxford University Press, ISBN 0-19-850481-0).

Because we now operate with much stronger magnets than in the old CW days, the way that we generate the magnetic field has changed. Permanent magnets are not strong enough for fields above 90 MHz and conventional electromagnets would consume far too much electricity to make them viable (they would also be huge in order to keep the coil resistance low and need cooling to combat the heating effect of the current flowing through the magnet coils). The advent of superconducting wire made higher fields possible.

(The discovery of superconduction was made at Leiden University, by Heike Kamerlingh Onnes back in 1911 while experimenting with the electrical resistance of mercury, cooled to liquid helium temperature. His efforts were recognised with a Nobel Prize for Physics in 1913 and much later, a crater on the dark side of the moon was named after him. The phenomenon was to pave the way to the development of the very powerful superconducting magnets that we have today.)

Superconducting wire has no resistance when it is cooled below a critical temperature. For the wire used in most NMR magnets, this critical temperature is slightly above the boiling point of liquid helium (which boils at just over 4 Kelvin or about -269°C). (It should be noted that new...