# 2D NMR Experiments


## The experiment

When $$\omega_1 \neq \omega_o$$: There is no interaction between the field $$B_1$$ and µ (they are not in accord) and the precession is kept around the axis Oz.

When $$\omega_1 \approx \omega_o$$: $$B_1$$ and $$\mu$$ are in accordance. Thus the couple applied by $$B_1$$ modifies the angle $$\alpha$$ of µ with Oz, and then causes transitions between the magnetic sublevels.

There is resonance. The value of the z magnetization decreases and it appears, in the $$y$$ direction, the transverse magnetization $$M_y$$.

## The Rotating Coordinate System

Impulsion angle and position of the $$\vec{M}$$ vector (Figure $$\PageIndex{1}$$) is given by the following relation , with $$B_1$$ which represents the amplitude or the power of the impulsion and tp the width or duration of the impulsion. It is possible to make these two values vary together in such a way that particularly interesting rotation angles appear. One of these is the angle $$\alpha = 90^o$$.

In this case all the magnetization is orientated in the plane xy and the signal reaches its maximum of intensity. (7)

An other angle allows the inversion of the M vector by the application of an impulsion or = 180°. In this experiment, the vector M is orientated in –z. Practically, one uses the angle = 45° in order to get a good compromise between measurement time/quality of the response.

## The Free Induction Decay Signal

The signal given by the receiver coil is known under the name of interferogram: Free Induction Decay (FID). In opposition to the continue wavelength signal, the time dependent signal we monitor in this case is an emission signal, because the radiofrequency field B1 is turned off upon the signal acquisition. The experiment gives us practically a variable field which is linear at high frequency following the y axis. In fact it is an oscillator or an emitter with the Larmor frequency of the nuclei under study (7) .

The time signal S(t) generated in the receiver coil by the xy component of M weakens under the relaxation process.

## The notion of phase cycle

The phase cycles or phase programs allow to:

• choose the relevant signals and to neglect these ones which do not contain information and which, eventually, are susceptible to hide some other useful signals.
• discriminate the sign of the frequencies in the fl dimension.
• compensate the inhomogeneity from one or several impulsion in the sequence,
• to achieve an optimal quadratic detection in the f2 axis. (5)

Any impulsion in a sequence has its own phase cycle which may be more or less complex. The ideal number of scans must be a multiple of the phase number of the longer cycle. For a better understanding of this method, a standard nomenclature has been defined (Fig. 7).

##### Example $$\PageIndex{1}$$: The Cyclops Cycle

= x,y,-x,-y. 0,1,2,3. This cycle involves the accumulation of a multiple of 4 numbers between each free precession.

The first impulsion B1 occurs around the x and the emission will occur in the y axis, the third impulsion along the - x and the reception in -y, etc.

There are other variations of this cycle like the following:

$\Phi = x,-x, y,-y$

or

$\Phi = 0,2,1,3.$

or still:

$\Phi = x,x,-x,-x,y,y,-y,-y$

or

$\Phi 0,0,2,2,1,1,3,3.$

This last one implies a multiple of eight transient cycles in the accumulation.

## References

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2D NMR Experiments is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Marc Bria.