Spin Echos for Uncoupled Spins

The spin echo is one of the most fundamental building blocks for NMR pulse sequences. Its main purpose is to refocus chemical shifts. The simplest spin echo is that for uncoupled spins where only the offset, Ω (i.e. the frequency difference between the carrier and the resonance) need be considered. The pulse sequence is represented in the upper portion of the figure with the vector and product operator representations below. A 90_x pulse is first given to create magnetization along the -y axis of the rotating frame. During the first delay period, τ, the magnetization rotates in the x-y plane at a rate, Ω. The 180_x pulse rotates the magnetization 180 degrees about the x axis. During the second delay period, the magnetization again rotates in the x-y plane at a rate, Ω in the same direction as during the first delay. At the end of the second delay, the magnetization is on the y axis and the collection of the FID is started. It is important to note that the echo will always have its maximum at 2τ after the 90 degree pulse regardless of its offset, Ω or the duration of τ. The value of τ however is limited by the T₂.

What is T1ρ and How is it Measured?

The time constant for the build up of magnetization along the direction of the main magnetic field, B_o, (the z axis) either after a pulse or upon initially exposing a sample to the magnetic field is called the T₁ relaxation time or spin-lattice relaxation time. It is this relaxation time which determines the rate at which a pulse sequence can be repeated. The time constant for the decay of magnetization in the x-y plane of the rotating frame of reference after a pulse is called the T₂ relaxation time, the spin-spin relaxation time or the transverse relaxation time. It is this relaxation time which determines the natural line width of a particular resonance. There is another relaxation time constant of interest to NMR spectroscopists - T₁ρ. T₁ρ is the time constant for the decay of magnetization along the radio frequency field, B₁, of an applied spin locking pulse in the rotating frame of reference. It is analogous to T₁ except it describes relaxation along the radio frequency field of the pulse (which is static in the rotating frame) rather than relaxation along B_o. T₁ρ's are of interest in ROESY, TOCSY and cross polarization experiments. The T₁ρ is measured by first applying a 90 degree pulse to an equilibrium magnetization vector. A spin locking pulse is then applied. The phase of this pulse is shifted 90 degrees with respect to the excitation pulse such that the field of the spin locking pulse is coincident with the spin vector in the rotating frame of reference. During the spin locking pulse, the large magnetization vector (which was initially polarized in B_o) decays to its equilibrium value in the much smaller field, B₁, with time constant, T₁ρ. The T₁ρ is measured by analysing the intensity of the NMR signal in spectra collected as a function of the duration of the spin locking pulse. This is illustrated in the figure below.