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#### neorich2002

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##### Relaxation times as a function of temperature in NMR
« on: February 12, 2008, 02:54:41 PM »

Good Morning, I have been carrying out some NMR relaxation measurements (T1 and T2), and have found that they have a dependence on the temperature of the sample, for example T1 is small at lower temperatures, and larger at higher temperatures.

Can anyone explain why there is a dependence of these relaxation times on the sample temperature, in other words what is it about the sample properties at different temperatures that changes the values of T1 & T2?

Any help is much appreciated.

neorich2002
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#### Yggdrasil

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##### Re: Relaxation times as a function of temperature in NMR
« Reply #1 on: February 12, 2008, 03:17:31 PM »

Conceptually, relaxation times in NMR depend on the rotational correlation times (τc) of molecules in solution.  Wikipedia gives equations for the T1 and T2 relaxation times (http://en.wikipedia.org/wiki/Relaxation_%28NMR%29#Microscopic_mechanism) and as you can see τc appears in both equations.  τc itself depends on temperature, following the relation:

$\tau_c = 4\pi \eta a^3 / k_bT$

where, η is the viscosity, a is the radius of the molecule, kb is the Boltzmann constant, and T is absolute temperature.

Since spin-lattice relaxation is caused by stimulated emission, T1 will be smallest (i.e. T1 relaxation will occur fastest) when the rotational fluctuations occur at a rate comparable to the Larmor frequency of the nuclei being manipulated (i.e. when τc ~ 1/ωo).  T2 (spin-spin) relaxation times behave more simply as they always decrease with increasing τc.

I hope this was a somewhat clear explanation.  Let us know if you are still confused.

P.S. in the future, please refrain from posting the same topic in multiple forums.  It is against the Forum Rules.  Thanks.

[edit: made the equation in LaTeX so it's more clear]
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#### neorich2002

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##### Re: Relaxation times as a function of temperature in NMR
« Reply #2 on: February 13, 2008, 02:51:29 PM »

Thanks Yggdrasil,