From a radio pulse to molecular motion
Atomic nuclei in a magnetic field behave like tiny magnets. A short radio-frequency pulse tips them, and the signal that follows fades as they lose their common direction (T2) and recovers as they return to equilibrium (T1). How fast this happens depends on how freely the molecules move, so a relaxation time is a direct, quantitative view of molecular motion.
A spin echo goes one step further. A second pulse refocuses the signal after a delay, and the echo that appears shows what is left of it. Following how the echoes shrink gives the decay time T2 without the effect of imperfections in the magnet.
Inverse Laplace analysis: many motions, one decay
Real samples rarely relax with a single time. A mixture, a gel or a porous solid holds several populations of molecules at once, and their signals add up in one decay. The inverse Laplace transform (ILT) is a mathematical technique that takes this single decay and turns it into a distribution of relaxation times, with a separate peak for each population.
What makes it powerful is that no model has to be assumed beforehand. Instead of deciding in advance that there are two components and fitting two exponentials, the data show how many populations are present and how much each contributes. The same approach works for T1, for T2 and for diffusion decays.
In two dimensions it becomes even more informative. Measuring, for example, T1 and T2 together, or diffusion and T2, and inverting in both dimensions gives a map in which populations that overlap in one dimension are pulled apart. Researchers use such maps for food, rocks, polymers, gels and biological tissue, and they make an excellent subject for a graduate project.
For students it is also an introduction to inverse problems, where a little noise can change the answer, and to the role of smoothing in solving them.
Session ideas
- Calibrate a 90° and a 180° pulse, and watch the free decay. Level: undergraduate
- Record a spin echo and a train of echoes to measure T2. Level: undergraduate
- Measure T1 by inversion recovery. Level: undergraduate
- Measure relaxation times in a series of glycerol and water mixtures and plot them against viscosity. Level: undergraduate
- Add a small amount of a paramagnetic salt and see how it shortens the times. Level: undergraduate and above
- Record the decay of a mixture of two liquids, fit it with one and then two exponentials, and compare the result with an inverse Laplace transform. Level: graduate
The impurity experiment is also a good lesson in experimental design. Keep the temperature, the sample volume and the position of the tube identical, so that a change in the result can be traced to the one thing that was changed.
What it adds to a teaching laboratory
- No cryogens and no dedicated room
- Small footprint and low running costs, with safe, ordinary samples such as oils, water and glycerol
- A session fits in an afternoon, so every group can run its own experiment
- Real data from real samples, instead of a simulation
Points that matter in practice
- Viscosity depends strongly on temperature, so the temperature of the samples must be controlled and recorded
- Use the same sample volume and tube position for every measurement, and calibrate the pulses at the start of each session
- Dissolved oxygen is paramagnetic and shortens the relaxation times of pure liquids, which is worth discussing with the students
- These instruments record how the signal decays in time. They do not give chemical-shift spectra
- Inverse Laplace analysis needs good signal quality and software that includes the inversion, so check its availability for your instrument
From first demonstration to a teaching routine
MSY Consulting demonstrates the experiments on your own samples, helps you select a set of sessions that fits your course, and trains the teaching staff, so that the practicals run on their own.
Let's talk about your application
Send an email describing your instrument and your application, and you will get a reply.
contact@msyconsulting.euMSY CONSULTING SAS · Wissembourg, France · LinkedIn