Copyright 2005, all rights reserved

Magic Angle Spinning (MAS) and Nuclear Magnetic Resonance (NMR) Made Simple by F. David Doty

F. David Doty, Doty Scientific, Inc., Columbia SC

The nuclei of many important atoms are actually very small magnets (because they have a property called spin).  Of course, the nucleus also has mass, and a spinning mass gives rise to angular momentum.  A spinning top also has angular momentum, and a property of angular momentum is it wants to maintain its direction – that’s the reason a spinning top resists tipping over, even if pushed.  Instead, it will precess (wobble) about the vertical axis as a result of the interaction of gravity with its angular momentum.

When a collection of magnetic nuclei (for example, the hydrogen nuclei in a grain of sugar) is placed in a large magnetic field, that field exerts a torque on these nuclei, which tries to align them with the field (like trying to tip the top over).  But instead of immediately aligning, the nuclei precess and slowly come into alignment.  The precession or resonant frequency of a nucleus depends on the atom's type (¹H, ¹³C, etc.) and the precise magnetic field at its location.

What makes this interesting is that the frequency of precession can be measured extremely precisely – meaning, to within one part in a billion – under the right conditions, and the precise measurement of that precession frequency and the rate at which the nuclear magnetic field amplitude (induced in the pickup coil) decays or “relaxes” allow for a very precise determination of the micro-environment. 

The various hydrogen nuclei in a complex molecule will all have very slightly differing precession frequencies and decay rates because they are in slightly different magnetic fields, owing to the minor effects of their neighboring atoms, though they’ll all be very close.  Hydrogen atoms in a 14 T field all resonate at about 600-MHz --- within a few parts per million.   The same applies to the carbon atoms, except they’ll all be fairly close to 150 MHz and their spread may be a hundred parts per million.  And so on for the other atoms.

If we dissolve our grain of sugar in water, the sugar molecules are rapidly and randomly tumbling, and the first hydrogen atom on each sugar molecule all resonate at the same average frequency, the second hydrogen atom on each sugar molecule all resonate at a second, slightly different frequency, and so on.  Analyzing the NMR spectra (the composite of graphs of all the resonances) allows the structure of the molecule to be determined – the distances between each atom, the angles between them, a complete 3D picture can be derived.

One technical problem is creating the external magnetic field with the incredible uniformity needed to measure the frequency so ultra precisely.  The external field may be slightly different (say, by 20 parts per billion) at different locations in the sample tube.  If we spin the sample, the various molecules go through slightly different external fields, but the average external field each sees is more nearly the same. 

The more non-uniform (inhomogeneous) the external field is, the faster we need to spin the sample for this averaging process to work.  With good magnets and liquid samples, it’s generally sufficient to spin the sample 20 revolutions per second, which we denote 20 Hz.  An important point to understand is that spinning the sample doesn’t necessarily spin the nuclei.  The nuclei are quite free inside each atom.  It’s the electron clouds that make up the structure that we know as material.  The nuclei just float inside it and give it mass.

Of course, some samples of interest (like membrane proteins) can’t be dissolved without being destroyed, and this causes major complications in NMR.  In solids, the individual molecules aren’t tumbling rapidly to give us the nice sharp signals we get from liquids.  And if the solid isn’t a crystal, every molecule is stuck in a different direction, so every molecule is singing in a different key, and the signal can’t be analyzed. 

Fortunately, there is a “magical” solution for solid samples.  We’re interested in the response of nuclei in the isolated molecule, but we can’t just listen to a single molecule.  We need the combined signals from trillions of molecules, all singing in the same key, to get a strong enough signal to analyze.  It so happens that when the angle between any two molecules with respect to the external magnetic field is a certain value, the so-called “Magic Angle”, or 54.7°, the magnetic interactions between those molecules vanish. 

We can’t put the entire sample along a microscopically fine line at this magic angle in the magnet, but we can make them all have this angle, on average, with respect to every other molecule in the sample if we spin the sample rapidly about this axis.  And that’s exactly what is done in Magic Angle Spinning, or MAS.  In order for it to work, the sample has to spin fast enough that the nuclei don’t relax much during a single revolution.  In practice, this often means the sample needs to spin at 10,000 to 25,000 revolutions per second.  This spinning doesn’t affect the orientations or energy levels of the nuclei.  It just makes each molecule in the randomly oriented powdered solid behave magnetically as though it’s the only molecule around and is oriented at this Magic Angle.  That makes the signals much simpler to analyze – like in a liquid. 

So there you have it.  Solid (rigid) samples must be spun at the magic angle at incredible speeds in NMR so that all the molecules in the sample sing in the same key.  Not the same note – it’s still an incredibly complex mix of closely spaced resonances, but at least it can be analyzed.  This allows us to get precise 3D pictures of the most complex biological macromolecules.

How do we do the spinning?  By using air bearings and microscopic turbines.  The faster we want to spin, the smaller the spinner must be, as the surface speeds must be limited to approximately the speed of sound or the sample will heat up too much and the stresses will cause the spinner to explode.  For example, a sample spinner of 4 mm diameter, when made of silicon nitride can spin 25,000 Hz, or 1.5 million rpm, without exploding.  Smaller spinners, with diameters as small as 1.6 mm in diameter, can spin faster, and this sometimes makes the signals even sharper.  Of course, the smaller the rotor, the weaker the signal, as there are fewer molecules reporting, so the longer it takes to decipher it.  And with really complex molecules, like large proteins, it can take weeks of listening even in a 4 mm rotor.

Are there other possible applications for the really cool ultra-fast micro-turbine technology, maybe energy related?  Perhaps, but that’s another story.