Zero-quantum relaxation time

Rotational resonance of inhomogeneously broadened systems was studied by Heller et al.ul With nonlinear least-squares fitting, the distance, the inhomogeneous broadening, the zero-quantum relaxation time, and their respective errors, can be obtained. For short distances, all three parameters can... 

Proton-driven spin diffusion (see also Appendix A) is the classical spin-diffusion experiment for low abundant spins. The line width of the one- and zero-quantum lines of the S-spins are mainly determined by the heteronuclear dipolar couplings while the homonuclear I-spin dipolar coupling makes the broadening of the levels homogeneous. Suter and Ernst [12] calculated an approximate value for the zero-quantum relaxation time... 

Reff = observed dipolar coupling constant t = time T20 = spin term in the spherical tensor representation of the dipolar Hamiltonian = zero-quantum relaxation time constant U = propagator = magne-togyric ratio of spin / A/ = anisotropy of the indirect spin-spin interaction 0 = angle between the applied field and the internuclear vector A = dephasing parameter /Uq = permeability of free space Vj. = rotor frequency in Hz 1/, = isotropic resonant frequen-... 

The method relies on the measurement of cross-correlated relaxation rates in a constant time period such that the cross-correlated relaxation rate evolves during a fixed time r. In order to resolve the cross-correlated relaxation rate, however, the couplings need to evolve during an evolution time, e.g. tt. The first pulse sequence published for the measurement of the cross-correlated relaxation rate between the HNn and the Ca j,Ha i vector relied on an HN(CO)CA experiment, in which the Ca chemical shift evolution period was replaced by evolution of 15N,13C double and zero quantum coherences (Fig. 7.20). 

Therein, cross-correlated relaxation T qHj c h °f the double and zero quantum coherence (DQ/ZQ) 4HizCixCjj generated at time point a creates the DQ/ZQ operator 4HjzCjJCiy. In the second part of the experiment, the operator 4HJZCjxQy is transferred via a 90° y-pulse applied to 13C nuclei to give rise to a cross peak at an(i... 

As an example of the measurement of cross-correlated relaxation between CSA and dipolar couplings, we choose the J-resolved constant time experiment [30] (Fig. 7.26 a) that measures the cross-correlated relaxation of 1H,13C-dipolar coupling and 31P-chemical shift anisotropy to determine the phosphodiester backbone angles a and in RNA. Since 31P is not bound to NMR-active nuclei, NOE information for the backbone of RNA is sparse, and vicinal scalar coupling constants cannot be exploited. The cross-correlated relaxation rates can be obtained from the relative scaling (shown schematically in Fig. 7.19d) of the two submultiplet intensities derived from an H-coupled constant time spectrum of 13C,31P double- and zero-quantum coherence [DQC (double-quantum coherence) and ZQC (zero-quantum coherence), respectively]. These traces are shown in Fig. 7.26c. The desired cross-correlated relaxation rate can be extracted from the intensities of the cross peaks according to ... 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

For positive lit electrodes one can register the drift of holes, and for negative ones- the drift of the electrons. The photosensitizer (for example Se) may be used for carrier photoinjection in the polymer materials if the polymer has poor photosensitivity itself. The analysis of the electrical pulse shape permits direct measurement of the effective drift mobility and photogeneration efficiency. The transit time is defined when the carriers reach the opposite electrode and the photocurrent becomes zero. The condition RC < tlr and tr > t,r should be obeyed for correct transit time measurement. Here R - the load resistance, Tr -dielectric relaxation time. Usually ttras 0, 1-100 ms, RC < 0.1 ms and rr > 1 s. Effective drift mobility may be calculated from Eq. (4). The quantum yield (photogenerated charge carriers per absorbed photon) may be obtained from the photocurrent pulse shape analysis. 

Figure 2 The four-level diagram for a system of two interacting spins, in this case an electron (S) and nucleus with a positive gyromagnetic ratio (/). The intrinsic electron and nuclear spin relaxation are given by p and w°, respectively, and the dipolar and/or scalar interactions between the electron and nuclear spin are represented by p, w0, w, and w2. The transition w0 is known as the zero-quantum transition, while w, is the singlequantum transition and w2 is the double-quantum transition. Nuclear and electronic relaxation through mechanisms other than scalar or dipolar coupling are denoted with w° — 1/Tio and p — 1/Tie, where Ti0 and T1e are the longitudinal relaxation times of the nucleus and electron in the absence of any coupling between them. Since much stronger relaxation mechanisms are available to the electron spin, the assumption p>p can be safely made. Adapted with permission from Ref. [24].

---