Flip-flop transitions

The negative sign for W0 in the second term reflects the fact that this flip-flop transition increases Iz while it decreases S. ... 

The decoupling efficiency depends on two factors [Engl, Mehl] (1) The amplitude (Oil = - y fii/ of the decoupling field in comparison with the strength of the heteronuclear dipole-dipole interaction. (2) The modulation of the heteronuclear dipole-dipole coupling by flip-flop transitions in the system of the abundant / spins, which communicate by the homonuclear dipole-dipole interaction. In addition to this, the influence of thermal motion has to be considered [Mehl]. 

Fig. 3.5.3 [Blii6] Spin diffusion denotes the seemingly random migration of magnetization through the sample by energy-conserving flip-flop transitions of spin pairs.

One approach to improve the electron-nuclear polarization transfer rate in ONP experiments is to adapt time-tested Hartmann-Hahn-type approaches. Groups at Heidelberg and Leiden separately developed similar approaches (respectively dubbed Hartmann-Hahn ONP (HHONP) and nuclear orientation via electron spin locking (NOVEL) ) whereby a spin-lock mw pulse sequence is applied to the electrons such that their frequency in the rotating frame matches the Larmor frequency of the H nuclei in the lab frame. Thus, the formerly forbidden electron/nuclear flip-flop transitions effectively become thermodynamically allowed , improving the efficiency of the polarization transfer compared to MIONP experiments performed outside this Hartmann-Hahn condition. The polarization transfer typically occurs on the ps time scale, generally faster than both the electronic T and the triplet lifetime. ... 

The different operating principle of generating nuclear spin polarizations, by electron-nuclear flip-flop transitions instead of by spin sorting, reduces the mechanism to a two-step scheme. 

Flip-flop transitions are bidirectional, so the precursor multiplicity is a key prerequisite, in the same way as for S-To-type CIDNP. 

Development of nuclear polarizations in the spin-correlated pairs or biradicals Because Equation (6) couples the nuclear spin motion and the electron-spin motion, not only the electron-spin state of each pair oscillates but also the nuclear spin state. Over the ensemble, however, the oscillation is not symmetrical because flip-flop fransifions are only possible for one-half of the pairs. Consider, for example, an ensemble of biradicals with one proton, and let the biradicals be bom in state F i). Taking into accoimt also the nuclear spin, one-half of fhe biradicals are fhus born in state T ia) and the other half in state T ijS). The latter cannot undergo flip-flop transitions to the singlet state, so have to remain in the state they were bom. The others oscillate between T ia) and I SjS). If a fracfion n of fhem has reached the singlet state, the total number of biradicals wifh nuclear spin a) is l-n)/2, and the total number of biradicals wifh spin jS) is n/2+1/2. The difference between the number of molecules wifh nuclear spin a) and jS) is fhus -n, in other words the system oscillates between zero polarization (n = 0) and complete polarization of one sort n = -1,... 

The polarization generation by flip-flop transitions instead of by spin sorting thus causes S-T i-type CIDNP to differ from S-To-type CIDNP in three main aspects. First, different exit channels are not needed. Second, even in cases when they are available, the polarizations from them are exactly equal. Third, the polarizations are always of one sort (one sign). 

It is at this point that S-To-type CIDNP and S-T i-type CIDNP diverge. Because there are no flip-flop transitions in the first case, a separation of nuclear and electronic subspaces is possible and leads to a drastic simplification of the problem, since only four elements of the density matrix have to be retained. This even affords a closed-form analytical solution if some simplifying assumptions are introduced. In the second case, no such separation is possible, and numerical solutions of the stochastic Liouville equation are the only feasible procedure this subject is obviously beyond the scope of this review. 

The situation is quite different with S-T -type CIDNP because nuclear spins are flipped in that case. Owing to the coupling of nuclear spin motion and electron spin motion, not only the electron spin state oscillates in such a system but also the nuclear spin state. Since, however, one-half of the pairs or biradicals cannot participate in this because their nuclear spin state does not allow an electron-nuclear flip-flop transition, the oscillation is not symmetrical. Its turning points are zero nuclear spin polarization and 100% nuclear spin polarization of one sign only. In contrast, the distribution of nuclear spin polarizations between singlet and triplet members of the ensemble is symmetrical. As an example, consider an ensemble of biradicals, where each biradical contains a single proton. Let the ensemble be created in the state T >, and without initial nuclear spin polarization. Half of the pairs, namely those that have nuclear spin /J>, cannot undergo flip-flop transitions. The others oscillate between T a> and S/3>. When all of those happen to be in S/ >, every nuclear spin of the triplet biradicals and every... 

The question of whether there are other mechanisms leading to CIDNP besides the radical pair mechanism is of central importance because chemical conclusions that are drawn from CIDNP results on the basis of the latter mechanism might of course be entirely wrong with another mechanism being the source of the polarizations. There has been some evidence [67-72] that cross-relaxation in radicals, by which electron spin polarization (C1DEP) is converted into CIDNP, could provide such a mechanism. Depending on whether cross-relaxation occurs by flip-flop transitions (Am = 0) or by double spin flips (Am = 2), opposite or equal phases of CIDEP and CIDNP would result. Since the origin of the electron spin polarizations is usually the triplet mechanism, this cross-relaxational mechanism is sometimes referred to as the triplet mechanism of CIDNP. 

Figuring out the frequency of a given transition is simple. On a 500MHz instrument, the frequency is 500MHz and the frequency is 125 MHz. For the single quantum Wjh transition that involves only flipping the spin of the H, the frequency of the photons that will drive this transition is 500 MHz. If the spectral density function is not zero at 500 MHz, then the Wjh transition will he efficient and the dipolar relaxation mechanism will he an efficient relaxation pathway for the H. For the transition, the frequency is 125 MHz so in this case, having spectral density at 125 MHz will make the single quantum dipolar relaxation mechanism efficient. For the double quantum W2 transition that connects the ota and pp spin state combinations, spectral density at 625 MHz (vh + Vc) is required. For the zero quantum Wg transition (also called the flip-flop transition), spectral density at 375 MHz (vh Vc) is required to make the transition efficient.

Flip-flop transition. Syn. zero quantum transition, Wg transition, zero quantum spin flip. When two spins undergo simultaneous spin flips such that the sum of their spin quantum numbers is the same before and after the transition takes place. For example, if spins A and B undergo a flip-flop transition, then if spin A goes from the a to the p spin state, then spin B must simultaneously goes from the a to the p spin state. 

Natural membranes contain enzymes known as flipases which catalyse flip-flop transitions of specific phospholipids, from one side of the membrane to the other (Chapter 10.3). There are also enzymes which catalyse transfers between one membrane and another. In some cases, proteins are believed to be anchored to natural membranes via phosphatidyl inositol (both glycolipids and glycoproteins may be associated with some membranes) (Figure 11.6). 

The A term can be visualised as a field shift at a nucleus. The B term couples spins of opposite polarisation, enabling them to exchange polarisation states ( flip-flop transitions). For homonuclear spin pairs, neither of these change... 

The 2D spin diffusion NMR experiment allows us to examine further the spectral assigments obtained from the ID and the 2D J-resolved experiments [51]. It also provides new details concerning distribution of hydrocarbons in zeolite ZSM-5. Spectral spin diffusion in the solid state involves simultaneous flip-flop transitions of dipolar-... 

The O-DNP experiment requires irradiation at the electron Larmor frequency to saturate the electron transition. The enhancement arises from subsequent relaxation processes involving simultaneous reversals of I and S in opposite directions (flip-flop transitions, Wq), or in the same direction (flip-flip transitions, IT2). This is depicted by the energy level diagram in Fig. 3. Hausser and Stehlik introduced a phenomenological description using rate equations [37], based on Solomon s treatment of the OE. According to the Solomon equations [49], the rate equation for the expectation value of the nuclear polarization can be written as ... 

Flip-flop spin diffusion is a phenomenon specific for NMR. It does not matter with other techniques. Spin diffusion based on Zeeman energy conserving flip-flop transitions of dipolar coupled spins, that is interchange of spin-... 

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