Inversion Recovery
Longitudinal (Spin-Lattice) Relaxation Times (T1) are determined using the Inversion-Recovery pulse sequence (180 - tau - 90). In this experiment, the magnetization is first inverted with a 180 degree pulse. A variable delay (tau) follows the pulse followed by a 90 degree read pulse.  Relaxation experiments of this type (especially spin=1/2) are governed by molecular rotation, bond lengths and both intra- and inter-molecular interactions.

Acquiring accurate longitudinal relaxation times (T1's) for 13Carbon (13C) is not an easy accomplishment. While it is rather easy to run an inversion-recovery experiment to measure relaxation times, there are a few things to remember when setting up an experiment.

  • Make sure all resonances are equally excited. That is, if the pulse power is not high enough, some resonances far from the observe frequency may experience a reduced flip angle, resulting in a smaller observed signal.
     
  • Use a large data size (SI) to insure that the data is well digitized. If the number of data points in the spectrum is too low, there will not be enough points to accurately define each resonance, resulting in inaccurate integrals (and peak heights).
     
  • Use a long relaxation delay between pulses. Resonances that are not fully relaxed will give a weaker signal than fully relaxed resonances. The 13C nuclei in your compound will not all relax at the same rate, so if you pulse too rapidly the quickly relaxing resonances will appear stronger than the slowly relaxing ones. This is especially true for 13C. To be sure of obtaining accurate integrals, you need to set a delay equal to 5-7 times the longest expected relaxation time for the resonances of interest.
 
   
  • 1H Spectrum

  • data acquired and processed in about 11 seconds

   
 
  • Proton T1 via Inversion Recovery

  • All data acquired and processed in about 3 minutes

  • Automated data processing and stack plot via macro

 

 
   

  T1= 1.864601 sec
Rel. amp. at infinity = 1.75
Inversion = 89.33%

 

 
The data above were worked up using the NUTS program from Acorn NMR. Below are the equations (directly from the nuts manual) used to fit the data.
 

T13IR (3-parameter T1-Inversion Recovery)

y = A * { 1 - [ 1 + W * ( 1 - exp( -K/T ) ) ] * exp( -x/T ) }

where
T = T1 relaxation time
A = peak integral at time x >> T
K = total time between scans in the 180-tau-90 sequence (acquisition time + relaxation delay time)
x = delay time t in the 180-t-90 pulse sequence
W = -(integral at time x=0 / A)

The parameter W is determined in the fitting process, as inversion in this experiment is not always perfect. This gives better results than assuming that the integral at time x=0 is simply the negative of the integral for infinitely long x.

ref: G.Levy and I.Peat, J.Magn.Reson., 18, 500 (1978).

T1IR (Inversion Recovery)

y = A * { 1 - [ 2 - exp( -K/T ) ] * exp( -x/T ) }

where
T = T1 relaxation time
A = peak integral at time x >> T
K = total time between scans in the 180-t-90 sequence (acquisition time plus relaxation delay time)
x = delay time t in the 180-t-90 pulse sequence

ref: Levy et al, J.Magn.Reson., 11, 58 (1973).