Longitudinal two-spin order

So far, we have not considered the so-called longitudinal two-spin order, represented by the product operator9 2J ff, a quantity related to the polarization of nuclei A and B. This spin state can be created in different ways. The easiest way is probably to let the system evolve under the sole Jab coupling so as to obtain an antiphase doublet, for instance the B antiphase doublet represented by 2//Vf (corresponding to the two proton-carbon-13 satellites in an antiphase configuration). 

The difference compared to equation B 1.13.2 or equation B 1.13.3 is the occurrence of the expectation value of the operator (the two-spin order), characterized by its own decay rate pjg and coupled to the one-spin longitudinal operators by the tenus 8j aud 5. We shall come back to the physical origin of these tenus below. 

The remaining two are the longitudinal spin order, which results when the macroscopic z magnetization of one nucleus (e.g., H) is opposite depending on the microscopic z magnetization (a or P) state of the other nucleus (e.g., 13C), and the identity (1) operator, which simply represents the vast majority of spins that cancel each other out and play no role in NMR experiments. Longitudinal spin order can be viewed as an intermediate state in coherence transfer 2 US- 21-S- 2I-S.r = 2SX z. Like z magnetization, it is not affected... 

The final two product operators are the longitudinal spin order operator (2IZSZ) and the identity operator (1) ... 

Consider a spin system of two spins I and S in a static field Bq in order to understand the mechanism of the longitudinal and transverse... 

Relaxation is an inherent property of all nuclear spins. There are two predominant types of relaxation processes in NMR of liquids. These relaxation processes are denoted by the longitudinal (Ti) and transverse (T2) relaxation time constants. When a sample is excited from its thermal equihbrium with an RF pulse, its tendency is to relax back to its Boltzmann distribution. The amount of time to re-equilibrate is typically on the order of seconds to minutes. T, and T2 relaxation processes operate simultaneously. The recovery of magnetization to the equilibrium state along the z-axis is longitudinal or the 7 relaxation time. The loss of coherence of the ensemble of excited spins (uniform distribution) in the x-, y-plane following the completion of a pulse is transverse or T2... 

Spin-Lattice and Spin-Spin Relaxations. In order to determine the content of these crystalline and noncrystalline resonances, the longitudinal and transverse relaxations were examined in detail. It was first confirmed that the noncrystalline resonance of all samples is associated with Tic in an order of 0.45-0.57 s. Hence, the noncrystalline component of all samples comprises a monophase, in as much as judged only by Tic. However, it was found that the noncrystalline component of drawn samples generally comprises two phases with different T2C values amorphous and crystalline-amorphous interphases. The dried gel sample does not include rubbery amorphous material it comprises the crystalline and rigid noncrystalline components. However, the rubbery amorphous phase with T2C of 5.5 ms appears by annealing at 145 °C for 4 minutes. For the orthorhombic crystalline component, three different Tic values, that suggest the distribution of crystallite size, were recognized for each sample, as normal for crystalline polymers [17,54, 55]. The Tic and T2C of all samples examined are summerized in Table 6. 

---