Pulse sequenc INDEX

Fig. 10 ROCSA pulse sequence based on Cn symmetry. The rectangular blocks in black represent jt/2 pulses. The recoupling period (q) comprises k cycles of Cnln. Each complete cycle of Cnln spans n rotor periods (nzR). The rf phase of each Cq subcycle is set equal to 2nq/n, where q is an index running from 0 to n — 1. Within each Cq subcycle, azR and bzR indicate the position and the duration of the POST composite pulse, respectively. We find that the solution (a, b) = (0.0329,0.467) is a favorable choice for the suppression of the homonuclear dipole-dipole interaction. The bracketed and subscripted values indicate the pulse length and rf phase in radians, respectively. (Figure and caption adapted from [158], Copyright [2003], American Institute of Physics)...

With this much interest in polyethylene, many attempts have been made to use low frequency NMR in either the time domain or frequency domain to monitor and control the production more rapidly. Auburn International (now part of Oxford Instruments) developed a widely adopted system based on the time domain spectrometers [21]. In this case, sample preparation is no longer an issue since the system accepts either powder or pellets and no solvent is used. The Auburn systems determine crystalline and amorphous ratios, viscosity, melt index and molecular weight For other types of polymers, the list of advertised measurements include tacticity, rubber content, copolymer analysis, and various rheological properties. These values are determined by correlating several routine but laborious methods with the decay of the NMR signal under various pulse sequences. The man-hours... 

The upper indexes, 00), 01), 110), 111), are to emphasize that the corresponding operators only execute a true Hadamard gate when they act on the indicated states. The indexes 01, 12, and 23 indicate the pulse transition as indicated in Figure 4.2. However, the operators c), d) and e), g) can be implemented by a single pulse sequence if we use two-frequency pulses to excite simultaneously two transitions. For example, Uhj. = where 01-23 indicates a two-frequency selective pulse that act simultaneously on the transitions 01 and 23 see Figure 4.2, will implement a operation independently of the initial state. All the Hadamard transformations indicated in (4.2.11) are self-reversible. 

As stated in Sect. 7.1, the current in SWV is sampled at the end of each potential pulse and the net response (/fw) is given by the subtraction of the current corresponding to a pulse with odd index (forward current, if) and that of the following pulse with even index (reverse or backward current, if) (see Eq. (7.6)). By using the expression of the current for any pulse of a given sequence (Eq. (5.23)), the expression for the SWV response of a reversible electrode reaction at electrodes of any geometry is immediately derived [21] ... 

Strictly speaking, the a should carry an additional index indicating the phase of the particular pulse. In Eq. (7) we have dropped this index, and we have assumed that the first and last intervals of the m.p. sequence are free-evolution intervals. We may assess the quality of calculated... 

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