Carbon-13 longitudinal relaxation time

In 2-substituted adamantanes 25 both types of 8-positioned carbon atoms (8syn and 8 ) exist within one molecule (Scheme 37). Early measurements with limited spectral resolution (176) did not differentiate between their signals. Later (124,244), differences of up to 0.7 ppm were detected, and application of various independent methods, including addition of lanthanide shift reagents (245), determination of longitudinal relaxation times T, (246), and evaluation of deuterium... 

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

Cross-polarization is based on the notion that the vast proton spin system can be tapped to provide some carbon polarization more conveniently than by thermalization with the lattice (7). Advantages are two-fold the carbon signal (from those C nuclei which are indeed in contact with protons) is enhanced and, more importantly, the experiment can be repeated at a rate determined by the proton longitudinal relaxation time Tin, rather than by the carbon T c (I)- There are many variants (7) of crosspolarization and only two common ones are described below (12,20). 

The experiment is applied for the evaluation of C T, values. T, values are usually used to optimize insensitive C experiments, i.e. to adjust the length of the preparation time in other NMR experiments. To deduce structural information it is usual to interpret the dipolar part of the longitudinal relaxation time (T, ). To separate the dipolar contribution from the contributions of other relaxation mechanisms, it is necessary to perform further experiments (gated decoupling experiments) to evaluate the heteronuclear NOE values. T °° may be exploited in a qualitative way to differentiate between carbon nuclei in less or highly mobile molecular fragments. In a more detailed analysis reliable T, values can be used to describe the overall and internal motions of molecules. 

Fig. 18. Values of the kc jk-i ratio (evaluated from the experimental efficiencies of formation of the excited state) as a function of the solvent longitudinal relaxation time Ti. Data for 4-(9-anthryl)-V,V,3,5-tetra-methylaniline in acetonitrile (ACN), pro-pionitrile (PN), butyronitrile (BN), propylene carbonate (PC), sulfolane (TMS) and 7-butyrolactone (BL) solutions. Adapted from [153].

On these systems the C longitudinal relaxation times T of the C5Me5 moieties have been measured by means of the Torchia s pulse sequence [48]. The Ti( C) values obtained for ring carbons have been rationalized on the basis of two relaxation interactions (dipole-dipole and chemical shift anisotropy) modulated by the motions involving the permethylated cyclopentadienyl rings. Interestingly, a qualitative comparison between solution and solid state C relaxation data shows that the same relaxation mechanisms are operative in both physical states. 

Pulse sequences have been described adequately in the literature. In this paper CP or CP-MAS spectra cU e those obtained via the usual spin-lock CP method (24,25). Spectra relating to the longitudinal relaxation times for carbons (T ) were obtained via the method of Torchia (31). In these latter spectra, signals... 

Information on the local structure of polymers is not limited to proton-proton spin diffusion experiments. Spin diffusion among the carbons can also be used [97], However, because of the low gyromagnetic ratio and natural abundance of the carbon-13 nuclei, it is less efficient than proton-proton spin diffusion. At natural abundance, the rate of spin diffusion is usually too low to compete with the rate of spin-lattice relaxation in most polymers. However, an interesting exception is that of semi-crystalline polymers such as linear polyethylene and cellulose which have very long longitudinal relaxation times and for which natural-abundance spin... 

Longitudinal Relaxation Time of Carbon Atoms for Tri-Butylphosphate (TBP) in Liquid and Supported on TVEX (50%TBP)... 

Longitudinal Relaxation Time (sec) Carbon Atom System C-1 C-2 C-3 C-4... 

Under conditions of proton decoupling there are two relaxation parameters of general interest the longitudinal relaxation time, and NOE, the nuclear Over-hauser enhancement. The third relaxation parameter, T2 or spin-spin relaxation time is not readily measurable for in decoupled systems. Both and NOE are directly related to the transition probabilities associated with nuclei changing energy levels. However, their functional dependence on transition probabilities differs and they can therefore be used in combination to resolve ambiguities. NOE has been found to be a very sensitive measure of mobility of carbon atoms of proteins and to provide reliable qualitative measures of the state of carbon atoms [3]. 

Further interesting is azacalix[4]arene 13b with a 1,3-alternate conformation, which has been demonstrated to be inflexible in solution [33]. Conformational behavior of 13b in solution was examined by means of relaxation time measurements (Fig. 10). A much smaller longitudinal relaxation time of 1.03 s was observed for the aromatic protons of 13b, as compared with 2.51 s reported for conformationally flexible p-fert-butylthiacalix[4]arene [34], demonstrating that the 1,3-conformation of 13b was inflexible in solution. This result was further supported by two additional experimental facts. First, NMR spectra of 13b were temperature independent [22, 33]. Second, the observed nuclear Overhauser effects were properly explained by considering a sole contribution of an inflexible 1,3-conformation of 13b [22]. X-ray crystallographic analysis revealed that a small annulus of 13b was responsible for the conformational immobilization by the small, but yet sufficiently bulky 0-methyl groups [33], which were too small for carbon-bridged calix[4]arenes to keep their conformations in solution [1,3,35,36]. 

As we shall see, all relaxation rates are expressed as linear combinations of spectral densities. We shall retain the two relaxation mechanisms which are involved in the present study the dipolar interaction and the so-called chemical shift anisotropy (csa) which can be important for carbon-13 relaxation. We shall disregard all other mechanisms because it is very likely that they will not affect carbon-13 relaxation. Let us denote by 1 the inverse of Tt. Rt governs the recovery of the longitudinal component of polarization, Iz, and, of course, the usual nuclear magnetization which is simply the nuclear polarization times the gyromagnetic constant A. The relevant evolution equation is one of the famous Bloch equations,1 valid, in principle, for a single spin but which, in many cases, can be used as a first approximation. 

Carbon nanotubes have been also used as a macromolecular scaffold for Gdm complexes. An amphiphilic gadolinium(III) chelate bearing a C16 chain was adsorbed on multiwalled carbon nanotubes (264). The resulting suspensions were stable for several days. Longitudinal water proton relaxivities, r] showed a strong dependence on the GdL concentration, particularly at low field. The relaxivities decreased with increasing field as predicted by the SBM theory. Transverse water proton relaxation times, T2, were practically independent of both the frequency and the GdL concentration. An in vivo feasibility MRI study has been... 

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