12C/13C Isotope Effects on 1H T1 Relaxation Times

What is the ¹H T₁ relaxation time of chloroform?  It seems like a simple enough question, but the answer is not so simple.  The relaxation rate for any proton is the sum of relaxation rates resulting from several different mechanisms (eg. homonuclear dipolar coupling, heteronuclear dipolar coupling, chemical shielding anisotropy, spin rotation etc...).  Each of these mechanisms of relaxation depends on dynamic effects and the extent to which those processes occur at the Larmor frequency.   Often, in proton-rich organic compounds, ¹H T₁ relaxation is dominated by the homonuclear dipolar coupling interaction.  For chloroform, with only a single proton, there can be no intra-molecular homonuclear ¹H dipolar interaction and the ¹H relaxation rate must depend on other mechanisms.  One of these mechanisms is the result of the heteronuclear dipolar coupling interaction.  For the ¹³C isotopologue of chloroform, one would expect a significant heteronuclear dipolar interaction between the directly bound ¹H and ¹³C.   This interaction is absent in the ¹²C isotopologue and one would therefore expect the T₁ relaxation time of ¹³CHCl₃ to be much shorter than that of ¹²CHCl₃.  This is illustrated in the figure below.

The ¹H T₁ relaxation times for both ¹²CHCl₃ and ¹³CHCl₃ were measured with the inversion recovery method for a degassed, dilute (1%) sample of chloroform in acetone-d6.  The inversion recovery delay was varied from from  1 sec. to 300 sec.  The recycle delay was 300 sec.  Relaxation is much more efficient for ¹³CHCl₃ compared to ¹²CHCl₃.  The T₁ for ¹³CHCl₃ is only 46% that of ¹²CHCl₃, indicating the significance of the heteronuclear ¹H - ¹³C dipolar coupling interaction as a relaxation mechanism.       

T1 Anisotropy

In the solid state, in the absence of magic angle spinning, the frequency of NMR lines depends on the orientation of the molecules with respect to the static magnetic field. For powdered samples, all orientations are represented in the sample and one obtains a broad envelope of peaks resulting from all possible orientations. Such broad resonance are called powder patterns and are said to be anisotropic. The frequency is not necessarily the only orientation dependant parameter. In some cases, the T₁ relaxation time also depends on the orientation of the molecules with respect to the magnetic field. In such cases the T₁ is said to be anisotropic. In contrast to the NMR resonances in solution which are characterized with a single T₁, the powder pattern can be characterized with many different T₁ relaxation times. Furthermore, the presence or absence of anisotropy in the T₁ can help discriminate between certain types of molecular motion. An example of an anisotropic T₁ is illustrated in the figure below for the wide line ²H inversion recovery spectra of acetone-d6 trapped in an organic inclusion compound. The line shape indicates that the acetone molecules undergo both fast methyl group rotation and fast two-fold flips about he carbonyl bond. One can see that the entire powder pattern does not have the same T₁ as the line shapes are a function of the inversion recovery delay, tau. The T₁ depends on the frequency within the powder pattern which in turn depends on the orientation of the molecules with respect to the magnetic field.

Resolution of Overlapping Signals Based on T1's

When students are asked what defines an NMR signal, they will most often say: the chemical shift, the coupling pattern, and the line width. One parameter which is often overlooked is the T₁ relaxation time. The T₁ is the time constant for the build up of magnetization along the magnetic field direction (z axis) when a sample is first placed in a strong magnetic field or after a pulse has been applied. It governs how long a spin system takes to come to equilibrium. T₁'s are measured with a 180-tau-90 inversion recovery sequence as a function of tau. For each resonance in an inversion recovery spectrum, there is a value of tau for which the signal will be nulled. If two signals with different relaxation properties overlap one another, tau values can be found which will null each of the signals individually and thus reveal the other signal. An example of this is shown in the figure below where the overlapping ¹H signals of the methylene protons one either side of the carbonyl group of 3-heptanone are examined (i.e. those in the 2 and 4 positions). The black trace in the bottom panel is the ¹H spectrum of the overlapping signals. The blue trace in the middle panel is an inversion recovery spectrum (phase corrected by 180 degrees) where a 4.1 second delay was employed. This delay nulls the protons on the 4 position revealing the quartet in the 2 position. The red trace in the top panel is an inversion recovery spectrum where a 5.5 second delay was employed. This delay nulls the protons on the 2 position revealing the triplet in the 4 position.

T1 Measurements and Estimation

T1 relaxation time measurements are usually done with a simple 180 -tau -90, inversion recovery pulse sequence (see figure). Tau is varied from a small value to a large value and a nonlinear regression is carried out to fit the best T1 value.These measurements can be very time consuming. One can get a reasonable estimate of the T1 much more quickly. Follow these simple steps:

1. Call up the pulse sequence "t1ir1d" (Bruker) or "s2pul" (Varian).

2. Set p1 and p2 (Bruker) or PW and P1 (Varian) to the 90 degree and 180 degree pulses , respectively.

Set the recycle delay, d1 (Bruker and Varian) to something you believe is much longer than the T1.

3. Set tau to a very small value (3 microseconds for example). Tau is d7 on a Bruker spectrometer or d2 on a Varian spectrometer.

4. Collect a spectrum and phase it such that all peaks are negative (one scan is often enough for protons). Store the phase correction.

5. Repeat step 3. increasing d7 (Bruker) or d2 (Varian) until the peak of interest is nulled. If the peak is negative, tau is too short. If it is positive, tau is too long.

6. The T1 of the peak of interest is the tau value for the null divided by the natural log of 2.