Nuclear Overhauser effect spin diffusion

Key Words Carbon-13 spin relaxation, T, Measurements, Nuclear Overhauser effect, Rotation-diffusion tensor, HOESY experiments... 

Several different analytical methods are needed to determine the structure and dynamics and to map the intermolecular interactions that prevail in supramolecular systems in solution [1]. NMR is one of the most powerful of these methods [Id-e]. The conventional NMR parameters that are used to characterize the structure and dynamics of supramolecular systems in solution are chemical shifts, spin-spin coupling, relaxation times, NOEs (Nuclear Overhauser Effect) and the correlation thereof. We shall demonstrate that the diffusion coefficient, which is currently underused, should be added to this arsenal of NMR parameters when characterizing supramolecular systems in solution. 

The essential features of the Overhauser effect and related relaxation phenomena can be seen by considering the transitions between the energy levels of a two-spin system consisting of a nuclear spin I and an electron spin S. Although this may appear to be a drastic oversimplification for describing the interactions in a solution containing free radicals, the rapid random diffusion of the molecules ensures that the solvent molecules are near a free radical many times during the nuclear relaxation time, and therefore any nucleus in solution may be considered to be in continuous interaction with an electron. 

On the dynamics of the neutral soliton, in 1980 Nechtschein and co-workers have demonstrated the evidence for the rapid diffusion of the neutral soliton along a one-dimensional chain from the observation of the pure Overhauser effect (OE) in trans-PA using a dynamic nuclear polarization (DNP) experiment and from the l/v frequency dependence of the H NMR spin-lattice relaxation rate 7Yil [143]. These observations give quantitative estimations that the pure OE implies the condition T (iJc 10" rad/s for the... 

Good evidence for the rapid motion and trapping of the soliton is demonstrated by a DNP experiment as shown in Figure 6.30 [146,173]. The dynamic nuclear polarization (DNP) experiments are carried out at 9 GHz between 1.5 and 300 K in cis [143,174] and irons PA [143,145,146,173,174]. At room temperature the pure Overhauser effect (OE) was observed in a -irans-PA without air or oxygen but a mixed solid state effect (SSE) together with OE was found in c/s-rich PA without air [143,174] and al -lrans-PA with air [146]. In particular, below 150 K, the mixed effect was observed, even in a -trans-PA without air [145,173], The OE is characteristic of dynamic interaction between nuclear spins and electron spins, with rapid motion, On the other hand, the SSE is of the static interaction between them. In other words, observation of the pure OE is clear evidence for the electron spin for motion with an inverse of the correlation time comparable with or larger than Wj,. At 300 K, the pure OE observed in all-/ra s-PA, is consistent with the conclusions for the neutral soliton to diffuse rapidly compared with 1/We as concluded from the ESR linewidth narrowed by motion [53] and the proton NMR 7Y ] [143] as a function of frequency over a broad range. 

After having demonstrated that the spins were moving in undoped rrflU5-(CH)., the aim of the researchers was to characterize the motion. Use was made of various methods described in section III. At first, as suggested by the polymeric nature of (CH), the motion was expected to proceed essentially along the chains. Evidence for the 1-D feature of the motion was given from the tu dependence of the nuclear relaxation rate Ti (u It should be noted that such a frequency dependence could also be obtained in the case of nuclear relaxation induced by fixed electronic spins and transmitted by nuclear spin diffusion. However, this alternative explanation for TL 3c w was invalidated by the Overhauser effect, which proved that the electronic spins were not fixed. Let us stress that the same spins are responsible for both the Overhauser effect and the nuclear relaxation. Further data supported the 1-D nature of the motion (1) The w - dependence was also observed for the electronic spin relaxation [41] and (2) the ESR lineshape was shown to display 1-D features, namely the Fourier transform of G(t) exp [24,25,36]. 

Spin dynamics studies in poly pyrrole-perchlorate (PPy-CIO4) have been performed by Devreux and Lecavellier [8]. At first, observation of the Overhauser effect proved the existence of a direct dynamic coupling between electronic and nuclear spins [104]. The frequency dependence of the proton relaxation rate is shown in Fig. 5.19. The data can be fitted with Ti" a for temperatures r < 150 K. For T > 150 K, the data deviate from 1-D diffusion behavior. They also cannot be fitted with the law of a pseudo-one-dimensional diffusion [Eq. (10)] with the introduction of a cutoff frequency o>c. Instead, they can be accounted for by taking the spectral density... 

---