Dead Time and Phase

The phase of an NMR peak depends on the sine/cosine character of the free induction decay (FID) when the receiver is turned on.  Positive and negative cosine FIDs will yield positive and negative in-phase peaks, respectively whereas positive or negative sine FIDs will yield peaks 90° out of phase.  FIDs that are neither a pure sine nor pure cosine with yield peaks which are out of phase to an extent dependent on the cosine/sine character of the FID.  In a perfect world, the receiver is gated on immediately after a perfect 90° pulse and all FID’s are cosines producing positive in-phase NMR peaks.  In the real world however, there are problems with acoustic ringing, pulse breakthrough imperfect pulses of finite duration and finite electronic switching times.  These problems produce a dead time between the end of the pulse and time at which the receiver is gated on during which data cannot be collected.  As a result the FID may not be a perfect cosine function and a phase correction will need to be applied after Fourier transform.  The first two figures below illustrate this point for a single off-resonance NMR signal as the dead time is increased.  The first figure shows the FID’s as a function of increasing dead time from bottom to top while the second figure shows the Fourier transformed spectra without phase correction as a function of dead time from left to right.

When there is more than one signal, the FID is an interferogram representing the sum of all time domain signals, each with a different frequency.  Since each component has a different frequency, its phase is affected to a different extent as a result of the dead time.  Higher frequency time domain components  (i.e. those representing peaks further off-resonance) are affected more than lower frequency components (i.e. those representing peaks closer to being on-resonance).  This is illustrated in the figure below for the ¹H NMR data for p-xylene.  The left-hand portion of top panel of the figure shows the FID containing both methyl and aromatic components while the right-hand portion of the top panel shows an expansion of the initial portion of the same FID.  The bottom panel of the figure shows a stacked plot of the NMR spectra collected as a function of dead time.  One can see that the phase of the aromatic peak furthest off-resonance is affected to a greater extent by an increased dead time than the methyl peak closer to resonance.

The last figure also shows a stacked plot of the ¹H NMR spectra of p-xylene as a function of dead time.

In this case, the methyl signal was set on-resonance.  One notices immediately that the phase of the on-resonance methyl peak is unaffected by an increase in the dead time whereas that of the off-resonance aromatic peak is severely affected.  The on-resonance methyl peak is not affected by an increase in dead time as its time domain signal is a simple exponential with no sine/cosine oscillations.  A loss of the beginning of a simple exponential FID due to the dead time still leaves a simple exponential and thus the phase is not affected.

Thank you to Dr. Michael Lumsden of the NMR Facility of Dalhousie University for suggesting the subject of this post.