Some theoretical aspects of chemically induced dynamic nuclear polarization

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Abstract
An analysis of aspects of the theory of chemically induced dynamic nuclear polarization (CIDNP) is given in terms of rigorous numerical solutions to the stochastic Liouville equation, in accordance with the methods previously developed for CIDEP. This analysis includes not only a model in which the exchange interaction is of finite extent in the spin Hamiltonian (EFA model) but models in which the exchange interaction explicitly affects the reactive trajectories (EFP model) by their inclusion in a spin‐dependent diffusion equation and in which charge interactions between reacting ionic radicals and their surroundings are accounted for in the Debye‐Hückel fashion. Several useful and simple relationships are found for the CIDNP phenomenon, and their dependence upon the model is discussed. It is found that the CIDNP polarizations are readily described in terms of two fundamental parameters‐Λ, the spin‐independent probability of reaction of singlets per collision, which includes all re‐encounters, and F*, which measures the conversion from triplets to singlets for the whole collision. Exact relations for the CIDNP polarizations are given in terms of these two parameters and are found to be nearly independent of model. The parameter Λ is shown to be simply related to k(r), the singlet reaction rate when the radicals are in contact, and to τ1, the effective lifetime of the reacting pair. Simple expressions for τ1 are given for all the models, and these results are compared with those for the usual discussions of diffusion rates on chemical kinetics. It is found that for normal diffusion rates, F* obeys the relation (1/2) Qτ d , very similar to that first proposed by Adrian, where Q is half the difference in resonant frequencies of the radicals, and τ d =d 2/D with D the relative diffusion coefficient and d the distance of closest approach. This relation is not appropriate for viscous systems, and the correct results are given for such cases. The effects of the finite range of the exchange interaction and the longer range Coulombic interactions between radicals upon F* for the different models are also obtained. In particular, for EFA the finite range of exchange yields an ``excluded volume'' effect wherein singlet‐triplet mixing (or Q mixing) is ineffective. The model dependent effects upon F* are closely related to the recurrence probabilities, and further results are obtained implying a simple expression for the first encounter probabilities of separated radicals under the effects of the different interactions. The polarizations are related to the time‐dependent CIDNP intensities that one may observe for a typical scheme of radical production, reaction, and relaxation.