Radio Frequency Pulses

The sample is again subjected to a constant magnetic field but all the nuclei are excited by a very short radio frequency pulse. The frequency e (e.g., 400 MHz for a proton at 9.4 tesla) is applied over a period of several... 

Nuclear Magnetic Resonance. The iateraction of a nucleus with Bq is usually described usiag vector notation and models as ia Figure 2 where the bulk magnetization, Af, and the static field Bq are initially parallel to A radio frequency pulse is appHed ia the xy plane for a duration of t p.s,... 

Fig. 2. Interaction of nucleus (electron) with static magnetic field, Bq, where the bulk magnetization, M, is (a) parallel to Bq and to the -axis, and (b), upon apphcation of a 90° radio frequency pulse along x, M perpendicular to Bq and to the -axis. See text.

Precisely controllable rf pulse generation is another essential component of the spectrometer. A short, high power radio frequency pulse, referred to as the B field, is used to simultaneously excite all nuclei at the T,arm or frequencies. The B field should ideally be uniform throughout the sample region and be on the order of 10 ]ls or less for the 90° pulse. The width, in Hertz, of the irradiated spectral window is equal to the reciprocal of the 360° pulse duration. This can be used to determine the limitations of the sweep width (SW) irradiated. For example, with a 90° hard pulse of 5 ]ls, one can observe a 50-kHz window a soft pulse of 50 ms irradiates a 5-Hz window. The primary requirements for rf transmitters are high power, fast switching, sharp pulses, variable power output, and accurate control of the phase. 

FID Free induction decay, decay of the induction (transverse magnetisation) back to equilibrium (transverse magnetisation zero) due to spin-spin relaxation, following excitation of a nuclear spin by a radio frequency pulse, in a way which is free from the influence of the radiofrequency field this signal (time-domain) is Fourier-transformed to the FT NMR spectrum (frequency domain)... 

In the carbon-13 experiments so far discussed, only a single radio-frequency pulse has been used to irradiate the spin system. This gave us information on the chemical shifts of the carbon nuclei in the molecule. The coupled spectrum obtained using gated decoupling (1.2.2) told us how many protons are bound to any one carbon atom however, this experiment requires a lot of time. There are however other experiments which give us this information... 

Fig. 5 Radio frequency pulse sequences for measurements of Sj and Si in DSQ-REDOR experiments. The MAS period rR is 100 ps. XY represents a train of 15N n pulses with XY-16 phase patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M = Nt 4, N2+ N3 = 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to 9.6 ms. Signals arising from intraresidue 15N-13C DSQ coherence (Si) are selected by standard phase cycling. Signal decay due to the pulse imperfection of 15N pulses is estimated by S2. Decay due to the intermolecular 15N-I3C dipole-dipole couplings is calculated as Si(N2)/S2(N2). The phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted from [45])...

Exploitation of the TROSY effect is rather straightforward. In contrast to 15N-HSQC (Heteronuclear Single Quantum Coherence) or standard triple-resonance experiments based on 15N-HSQC, no radio frequency pulses or composite pulse decoupling should be applied on amide protons when HN spin is not in the transverse plane. Likewise the 15N decoupling should be... 

Another ingenious modification of the HNN-COSY scheme involves the replacement of the homonuclear 15N-COSY transfer by a 15N-TOCSY transfer [37]. As the homonuclear TOCSY transfer is twice as fast as the COSY transfer, a significant sensitivity increase is achieved. The application is, however, limited to cases where the 15N donor and acceptor resonances are at similar frequencies, so that the power of the 15N-TOCSY radio frequency pulses needed is not too strong. A very interesting application of this scheme was presented for the sensitive detection of very small (0.14 Hz, Tab. 9.1) h4/NiNi couplings in N1-H1 06=C6-N1 H-bonds of guanosine tetrads. 

Fig. 10.4 Experimental scheme for the 2D [ N. HJ-TROSY using single transition to single transition polarization transfer (box labeled ST2-PT). On the lines marked H and 15N, narrow and wide bars stand for nonselective 90° and 180° radio-frequency pulses, respectively. The delay t=2.7 ms (see text). The line marked PFG indicates the pulsed magnetic field gradients applied along the z-axis G, amplitude 30 G/cm, duration 1 ms G2, 40 G/cm, 1 ms G3, 40 G/cm, 1 ms ...

N,1H]-TROSY (Fig. 10.4), 15N evolves and no pulses on 1H are applied (for completeness, radio-frequency pulses on 15N or a short 360° pulse on 1H during the 15N-evolution would not destroy the TROSY-effect). 

In the slow tumbling limit in the absence of radio frequency pulses only terms with /(to = 0) = need to be retained. The contribution of the DD coupling is... 

The theory of nuclear spin relaxation (see monographs by Slichter [4], Abragam [5] and McConnell [6] for comprehensive presentations) is usually formulated in terms of the evolution of the density operator, cr, for the spin system under consideration from some kind of a non-equilibrium state, created normally by one or more radio-frequency pulses, to thermal equilibrium, described by Using the Bloch-Wangsness-Redfield (BWR) theory, usually appropriate for the liquid state, we can write [7, 8] ... 

A In the simple homonuclear one pulse experiment, for the measurement of I D spectra, the response of the spin system following a strong non-selective radio frequency pulse is acquired. The pulse sequence consists of a preparation and detection period only. 

Fig. 2.1. Preferred nuclear precession about the direction of the magnetic field (a) and the effect of a 90°. radio frequency pulse (b).

If a spin system in thermal equilibrium with the lattice (i.e. that described by the vector p,) is subjected, immediately prior to the moment t = 0, to a strong radio-frequency pulse, then, after the pulse ceases, the vector corresponding to the density matrix of the system becomes (23,99)... 

Relaxation. In addition to changes in chemical shift, changes in lineshape are often also observed. The lineshape of an NMR signal is directly correlated to relaxation. Relaxation is the time taken for nuclei to return to equilibrium after equilibrium has been perturbed by a radio-frequency pulse. In NMR, there are two main types of relaxation, namely 7) and T2. The theoretical details are beyond the scope of this chapter for an excellent discussion, readers should refer to Keeler (2005). It is simply enough for the reader to understand that both 7) (also called... 

Excite Signal Radio frequency pulse applied to the transmit... 

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