JBChemYear4ProjNotes

T1 Relaxation (Longitudinal Relaxation)

• The time taken for a proportion of the nuclei of a sample to align their spins with the magnetic field.
• This proportion is 1-(1/e)
• This is about 63%.
• At a value of 5× T1, the number of nuclei with aligned spins gets very close to its maximum value.
• T1 can be measured by the release of energy. This energy is released as it is energetically favourable to be aligned with the magnetic field. 
• The loss of energy is completed by collisions with other molecules, collisions with the lattice surrounding the material or electromagnetic decay.
• It can be called longitudinal relaxation as the nuclei decay to point in the same direction as the magnetic field. 
• Relaxation in ALL types of NMR have to be induced. For T1 this is often a case of another magnetic field fluctuating near the Larmor frequency in the transverse plane. 
• The applied magnetic field simply chooses the longitude that will direct the lowest energy spins, other local magnetic fields will cause relaxation.
• T1 relaxation is always accompanied by T2 relaxation 

T2 Relaxation

• Considered to follow first order kinetics.
• Has a simple exponential decay with time period of T2
• Ie the time required for the transverse magnetization to fall to 1/e (~37%) of it’s starting value.
• Once the radio frequency has been passed through the sample, we have a tiny fraction of the molecules that are now coherently pointing in the transverse direction. 
• These coherent spins form a NET magnetisation at 90° to the magnetic field but it’s not perfect.
• As with the Larmour frequency,  the NET magnetisation now moves in a circular fashion around the plane, with a frequency that is known as the Larmour frequency 
• It is this movement in magnetisation that the receiver picks up and converts into the decay signal.
• The decay happens as nuclei become scrambled and leave the coherent group resulting in a weaker signal.
• The decay can occur in a number of ways.
• The coherent molecules can decay in a similar fashion to T1 decay. Any interaction with its surroundings displaces the spin and knocks that nuclei out. This is known as T1 in T2 relaxation. 
• T2 relaxation does not always occur with T1. This can be known as secular contribution to T2.
• A molecule can be located near to a local magnetic field caused by something like an iron clump. This produces it’s own magnetic field and so the frequency now becomes w=g(B(local)+B0)  
• This means that eventually the molecule is no longer circling in phase and is pointless. Thus relaxation has occurred.
• Spin spin flip flop occurs randomly and has no effect on T1. The longitudinal and transverse motions swap and so it loses coherence and as a result relaxation occurs.

Larmour Frequency

• In a similar fashion to a clock, or a weight in a string (think mechanics circular motion), a magnetic moment will align with the field.
• As it relaxes into the field, it will initially spin around in a circle.
• From circular motion, frequency = 2(pi)r/T. 
• The Larmour frequency is also given by the geomagnetic ratio and the strength of the magnetic field 
• W=gB

Phase Coherence

• During the initial relaxation to the initial magnetic field, there is a NET nucleus consensus towards the longitudinal direction in which the magnetic field is pointing. 
• This is not coherent though as the other fields do not add up to cancel each other out.
• When the radio frequency wave is turned on, it is at right angles to the magnetic field. This forces only some of the spins to point in the transverse direction. Eg 90° to the magnetic field.  The other spins are now completely random and their NET spin cancels out. Therefore, we are left with a few nuclei but with a coherent spin 90° to the magnetic field.

1H Relaxation

• Consider a nucleus or an impaired electron to be an ideal dipole magnet. That is to have a north pole and south pole . These will have fields that will interact through space known as dipole-dipole interactions.
• Electrons are much stronger at inducing relaxation than protons. Therefore, electron -proton interactions will be much quicker than proton – proton interactions. 
• This interaction scales with respect to distance by  1/r^6 
• Rotation rates and how close they are to the Larmour frequency result in whether T1 orT2 will predominate.

Chemical Shift Anisotropy

• Chemical shift results from the differing quantity of protection afforded to the nucleus by the electron clouds. Electrons rotate fast around the nucleus producing a magnetic field that counters the magnetic field in which the molecule is placed. Electron rich centres are afforded more protection than those in electron poor areas.
• Chemical shift anisotropy arises when the molecule is not symmetrical and so results in a different shift depending on the direction of the field compared to the direction  of the molecule. This does NOT happen in liquids as the constant tumbling averages this out.
• Magic spinning in solid state NMR can average this out to a non zero but known value in order to increase the resolution of the spectrum.
• This is important when looking at biological systems where the attached water molecules cannot necessarily move when bound to a protein.
• It is also important in something like phosphorus NMR 

Molecular flow, translation and diffusion

• Relaxation can be caused by a change in the local surroundings of a molecule. A change in the gravity, the magnetic field (even if caused by the presence of a magnetized iron clump which increases the local magnetic field or something similar).
• Non uniform magnetic fields cause relaxation. This can be caused by foreign magnetic fields or the such like.

Chemical Exchanges

• Mostly with protons
• Protons can cause relaxation by simply swapping with other protons in neighbouring molecules. This can be accompanied by a change in structure or nothing at all.
• Relaxation is proportional to the square of the magnetic field.

Brownian Motion

The constantly and erratic path formed by molecules in a liquid as a consequence of collisions between molecules and general tumbling.

Water T1/T2 relaxation times

• Water relaxation times are generally very long. As they tumble so quickly, they have large spaces between each molecule compared to something like collagen. 
• Spin spin interactions and energy exchange between molecules are therefore comparatively slow when compared to tightly packed proteins such as collagen where energy exchanges are frequent and spin spin interactions are more common.