Dilute spins

Cross polarization is the technique routinely used for increasing the sensitivity in the NMR dilute spins, such as 13C, using the reserve of abundant spins which usually are H. 

The "decrease of the spin temperature means an increase of population difference between the upper and lower energy spin states and consequently an increased sensitivity of the NMR experiment. From Equation (25), the temperature of dilute spins has been lowered by a factor 7x/y1 h, that is, V4 when X = 13C. This means an increased sensitivity of the FID resonance experiment equal to about 4 for the 13C nuclei. Because the X signal is created from the magnetization of dilute nuclei, the repetition time of NMR experiment depends on the spin-lattice relaxation time of the abundant spin species, protons, which is usually much shorter than the spin-lattice relaxation times of the dilute nuclei. This, a further advantage of cross polarization, delay between two scans can be very short, even in the order of few tens of milliseconds. 

The majority of double-resonance solid-state NMR experiments involving spin-1/2 nuclei use transfer of nuclear polarization via dipolar cross polarization (CP) to enhance polarization of the diluted spins S with small gyromagnetic ratio ys and significant longitudinal relaxation time T at the expense of abundant spins I with large y, and short 7 [215]. Typically, CP is used in combination with MAS, to eliminate the line broadening due to CS A, as well as with heteronuclear decoupling. To achieve the / S CP transfer, a (n/2)y pulse is applied at the I spin frequency,... 

The behavior of the dispersion mode derivative is also consistent with a proton dilute spin system, since if only a small fraction of the possible lattice sites are randomly occupied the majority of the protons will experi-... 

Isotopes in low abundance have long spin-lattice relaxation times which give rise to poor signal-to-noise ratios. Sensitivity can be improved by using a technique known as cross polarization where a complex pulse sequence transfers polarization from an abundant nucleus to the dilute spin thereby enhancing the intensity of its signal. 

In the diluted spin system such as 13C and 29Si, homonuclear dipolar interactions are negligible because of the low natural abundance of nuclei under observation (S) in this case term HD describes dipolar interactions between unlike spins (I and S), which for 13C and 29Si are most frequently the neighboring protons ... 

The cross-polarization (CP), i.e. the transfer of I-spin polarization to the dilute spins (S), is a double resonance experiment in which the I and S spins are coupled by a certain interaction, determined by the cross relaxation time tb. From the dynamics of the CP process, usually described with the spin temperature concept, the following equation for the time dependence of S-spin polarization could be derived ... 

Further possibilities are offered by various two-dimensional NMR methods. For example, heteronuclear solid-state correlation spectroscopy (27) is capable of correlating the spectra of abundant and dilute spins in solids, simplifying spectral assignment and permitting determination of shielding tensors. Futhermore, spin diffusion among abundant spins can be directly observed by this method. 

Pines, A., Gibby, M. G., and Waugh, J. A. (1972). Proton-enhanced nuclear induction spectroscopy. A method for high sesolution NMR of dilute spins in sohds. J. Chem. Phys. 56, 1776-1777. 

Cross-polarisation (CP) is a solid-state NMR experiment designed to achieve a higher sensitivity for the rare nucleus through the transfer of polarisation, driven by the heteronuclear dipolar interaction, from an abundant ( ll) to a dilute spin (13 C).118 Transfer of magnetisation is possible... 

However, in all the papers mentioned above the authors analyzed only three-dimensional (3D) systems, while a two-dimensional (2D) case is also experimentally observed surfaces of various absorbers, heterogeneous catalysts, photocatalysts, etc. In [137], Fel dman and Lacelle examined the quenched disorder average of nonequilibrium magnetization, i.e., a free induction decay G(t) and its relative fluctuations for dipolar coupled homonuclear spins in dilute substitutionally disordered lattices. The studies of NMR free induction decays and their relative fluctuations revealed that the functional form of the disorder average (G(t))c depends on the space-filling dimentionality D of the lattice. Explicit evaluations of these averages for dilute spin networks with D = 1, 2, 3 were presented in [137] ... 

Pines A, Gibby MG, Waugh JS (1973) Proton-enhanced NMR of dilute spins in solids. J Chem Phys 59 569-589... 

Different models of CP kinetics have been developed. The simplest model of CP dynamics (I-S) was derived for homogeneous solids where the I-S heteronu-clear interactions are relatively weak and the /-/ homonuclear dipolar interactions are sufficiently strong to provide efficient spin diffusion. For the abundant-dilute spin system, the CP dynamics can be described by equation (6) ... 

Whereas the I-S model is simple to understand and is widely applied, it is not sufficient to describe the CP kinetics for solids with heterogeneous populations of the source spins. The I-I -S model takes into account the efficiency of spin diffusion, which relies on homonuclear dipolar interactions and proceeds through ffip-ffop spin transitions. The I-I -S model relies on the existence of different proton populations, denoted I for the protons directly bound to an 5 spin under study and I for the rest of the proton network. The CP proceeds in two steps. A fast rise of the intensity is observed initially due to the transfer of the magnetization to a dilute spin (I -S) by the abundant spins in close proximity followed by a slow rise of the intensity or damped oscillation. Several equations have been proposed to describe the CP kinetics the simplest... 

FIG. 4. Infinite dilution spin- lattice relaxation rate in NaBr dissolved in... 

The benefits are primarily an intensity enhancement of the dilute spin signal by a factor of 7 abundant/7 dilute and a reduction of the recycle time between experiments since the ratedetermining relaxation time is now that of the abundant species, rather than that of the rare spins. Usually, the relaxation of the abundant spins are much faster than the dilute spin relaxation (13). The cross polarization experiment may thus be repeated with much shorter intervals, leading to a further increase of the signal-to-noise ratio of the rare spin NMR spectmm within a given period of time. The effectiveness of the cross polarization experiment depends on the strength of the dipolar interaction between the abundant and rare spin systems, i.e. on the distance between the actual nuclei (proportional to r, where r is the distance between the abundant and the dilute nuclei) (11). The efficiency of magnetization transfer decreases extremely fast as the distance between the abundant and rare spins increase. One should emphasis, that under normal conditions, the CP experiment does not provide quantitative results. Finally, the cross polarization sequence does not influence the line width. 

Another technique often implemented in high-resolution SSNMR experiments is cross-polarization In a CP experiment, bulk magnetization is transferred from that of an abundant spin ( H) to that of a dilute spin ( C, Si, and so on). To accom-... 

These filters are usually employed to suppress strong and undesirable resonances, e.g. parent signals of isotopically diluted spin systems. In a typical experiment the undesirable magnetization is inverted and allowed to relax until the equilibrium state is reached. At this point the inverted magnetization is not observable and the basic experiment may be started. In the simplest case a jump and return inversion pulse or binomial pulses can provide the necessary selective inversion. A simple example of application of a T relaxation filter is the J/-BIRD (BI linear Rotation Decoupling) HMQC... 

The experiments based on proton detection of rare spin nuclei are usually the most sensitive methods of determining NMR parameters of magnetically diluted spin systems. Unfortunately, recording of 2D correlation maps is usually also a time consuming experiment, especially if wide spectral bands have to be covered in the indirectly detected dimension. The most frequently encountered situation is that only one or a few peaks are expected within a narrow spectral band. However, the position of this band is not known. Several attempts have been made to reduce the experimental time needed to perform such experiments. One approach would be to record a highly truncated data set and use the linear prediction [86,87] to reduce the effect of the data truncation on the appearance of the spectrum. This technique is now available with most... 

Finally, we have to address the problem of how we create observable magnetization for nuclei such as C, " Sn, Pb. In solids, T relaxation times of dilute spin-1/2 nuclei can be prohibitively long. Cross polarization (CP) from abundant nuclei with shorter T relaxation characteristics ( H) is then the method of choice. Amongst various CP techniques, Hartmann-Hahn CP has become the most popular method [lf,9d] often used in combination with MAS... 

Even with the line-narrowing techniques described earlier, NMR experiments on solids with dilute spin- /2 nuclei are still relatively unattractive on two principal counts. One is the lack of sensitivity due to their low net polarisation and the other is the relatively long spin-lattice relaxation time that is often encountered. In solids where both abundant (I) and dilute (S) nuclei coexist, polarisation transfer techniques can usually be used to overcome both these problems. There are many schemes to effect such a transfer but the most common technique is to create and then spin-lock transverse I-magnetisation. This experiment is best understood using ideas from spin thermodynamics. The magnetisation is given by Curie s Law (Eq. 2.21) and the temperature in... 

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