Flip-Flop Spin Diffusion

On the other hand, if a static tube really exists as anticipated in the tube/reptation model, the predictions for anomalous segment diffusion are adequate, of course, and can be verified in experiment. This will be demonstrated by considering linear polymers confined in nanopores. 

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- 

Up and spin-down states, is normally negligible compared to molecular selfdiffusion in liquids. However, with viscous systems with little motional averaging of dipolar coupling and with the aid of very strong field gradients, NMR diffusometry is able to detect this immaterial transport mechanism competing with molecular diffusion. Spin echoes can be attenuated on this basis just as with any other incoherent displacement process [181]. 

The effect is also evident in Fig. 42 referring to a polyethyleneoxide melt with an extremely large molecular weight, Mw=5,000,000. The time-depen-dent diffusion coefficient was evaluated in the low wave number approximation, Eq. 27, according to R t))=6D(t)t. The time-independent plateau appearing at times t 0.1 s was shown to be due to flip-flop spin diffusion [10, 12]. 

As a consequence, the proper evaluation of segment diffusion at long diffusion times turned out to be more complicated than often anticipated. However, even with flip-flop spin diffusion theoretically taken into account, it is not possible to fit the formulas predicted by the tube/reptation model to the experimental data with respect to both the time and molecular weight dependences in a consistent way and without assuming unrealistic parameters [12]. 

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The dipolar correlation effect is based on stimulated-echo signals [2] and therefore contains elements both of transverse and longitudinal relaxation. Flip-flop spin diffusion as well as material transport may contribute to the exchange mechanism identified this way. An interesting result of the dipolar correlation effect study is the temperature dependence of the fraction of the more mobile segments which was shown to obey the empirical law (see Fig. 39) [168]... 

At very high molecular weights, when the diffusion coefficient due to flip-flop spin diffusion of the order 10 m /s is getting comparable to the ordinary Brownian self-diffusion coefficient, a flatter chain length dependence of the effective diffusion coefficient is expected [10]. 

Fig. 42. Time-dependent diffusion coefficient measured in a polyethyleneoxide melt (M =5,000,000) at 353 K as a function of the diffusion time [12]. The data were evaluated according to Eq. 27. The Rouse relaxation time Tr and the tube disengagement time predicted by the tube/reptation model based on the neutron scattering value of the ratio (R ee)/M = 1.01x10 ° m mol/g [179, 180] are indicated. The broken line represents the power law D(t)(xr which, according to the tube/reptation model, should appear in the time interval above Tr as limit (III)de and not below (see Table 1). The time range where this power law appears and the value for Zr estimated on the basis of the tube/reptation model are not consistent with each other. The plateau of the experimental data for f 0.1 s is due to flip-flop spin diffusion which physically limits the detection of molecular displacements by NMR diffusometry...

The total proton frequency range that can be probed by NMR spin-lattice relaxation techniques is 10 Hz < v < lO Hz. For the present application, deuteron resonance selectively applied to perdeuterated polymers confined to the pores is superior to proton resonance which, unlike the situation in field-gradient experiments, is affected by signals from the matrix and flip-flop spin diffusion across the matrix. The deuteron fi equency range is shifted by a factor of 0.15 to lower frequencies. This frequency window largely matches the time scale of chain modes of polymers with medium molecular masses. 

For the dilute aH spins surrounded by a large number of the 2H spins, the heteronuclear aH-H dipolar interaction is dominant, lifting the spectral overlap between the 1H packets. H spin diffusion is driven by the flip-flop term of the 1H-1H dipolar interaction, which becomes secular in the presence of spectral overlap. Thus, spin diffusion would be accelerated if it had not been for the 1H-2H dipolar interaction. In order to confirm this prediction, they used another RF channel of the OPENCORE... 

Flip-flop. The transverse diffusion of phospholipids in a bilayer membrane was investigated by using a paramagnetic analog of phosphatidyl choline, called spin-labeled phosphatidyl choline. 

Exactly the same results were obtained with spin diffusion experiments performed at ZSM-39. Frequencies can be affected by spin diffusion between sites having different NMR parameters, when, for example, magnetization is transported through a solid by means of mutual spin "flip-flops" that can occur even in the absence of atomic or molecular motion. By monitoring the correlation among frequencies in the different dimensions of a multidimensional NMR experiment, it is possible to learn about the mechanisms and rates of reorientation and diffusion processes in solids (32). 

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.

Problem (2) is that the spin-lattice relaxation rate of C NMR, 77c. should obey (6.14) as H NMR 77,j does, if the neutral soliton diffuses whole the sample. To investigate a role of spin flip/flop diffusion through H and C Scott and Clarke have measured 77] and 77c ll samples enriched by various ratios of C to D ( ) 98 0 (2) 90 98 and (3) 20 98 [152]. They observed ... 

Eq. 9 leads to spin diffusion with the flip-flop rate limiting the observed T. Below 10 s, the relaxation for the A spin is limited by the relaxation sink, which corresponds to the bonded methylene carbon. The effect of the siqall deviation In the coefficients from 1.0 and 0.0 near t s 10 s is non-exponential recovery, with the negative coefficient leading to a curve which is concave downward. For the M spin, the decay Jumps from theX curve for correlation times <10 " s to the Xg curve for correlation times >10 s. 

As already mentioned in the Introduction, magnetic relaxation in the solid state may be governed not only by dynamic phenomena but there may also exist a contribution from static phenomena such as spin diffusion, which consists of mutual exchanges of spin state, or flip-flops , between strongly coupled nuclei that have the same precession frequency but antiparallel spins. This mechanism is explained in more detail in chapter 7. It does not involve any variation in the energy of the system. When it occurs, magnetic relaxation times cannot be interpreted in terms of local dynamics only, but the two contributions have to be separated. 

As discussed in section 6.3, relaxation times of solid polymers are not only determined by dynamic phenomena. There may exist a contribution from the static mechanism of spin diffusion. The probability for a flip-flop between two opposite 1/2 spins having the same precession frequency is a decreasing function of the distance between the spins. Moreover, for heterogeneous solids, the spin diffusion mechanism manifests itself in a particular way. When two proton populations have different spin temperatures at a given time, they will tend to a common spin temperature by spin diffusion. (The mechanism is described in more detail in chapter 7). Such a situation occurs during a Ti( H) or determination in a heterogeneous system. For example,... 

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