Biomedical Engineering Reference
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Depth of immersion of paramagnetic centers
Dynamic exchange interaction in solution. In solutions of low viscosity electron spin-
spin dipolar interactions between paramagnetics are averaged by fast rotation of
molecules and the short lifetime of the encounter complex and therefore are very weak.
When a “radica
” in solution encounters another paramagnetic species the broadening of
the Lorentian line of the radical is related to the rate constant of the exchange relaxation
The value of
l
also can be determined from the change in the rates of the
spin-spin
and spin-lattice
relaxation of a radical in the presence of a
paramagnetic species:
Since usually is more sensitive to spin-spin interaction than especially in
the region of slow rotation and in solids, this method widens the accessible range of
values (Likhtenshtein and Kulikov, 1977 Kulikov et al. 1983a; Hyde and Subczinski,
1989).
According to Salikhov et al. (1971)
where
is the rate constant of encounters in solution,
is the probability of spin
exchange in the course of life t
e of the encounter complex, is the geometric
steric factor, is the nuclear statistical factor and J is the exchange integral of
interaction in the encounter complex at the direct contact between the particles. Eq. 16 is
valid if (the differences between the resonance frequencies of the spins),
and the ion spin
If
im
is independent of J (strong exchange) and
In the case of weak exchange
and
Substituting the definition of J from Eq. (1.8), with
into Eq. (1.12) gives
This equation can be used for estimation of the distance of closest approach (or depth of
the paramagnetic center immersion),
if other factors in the equation are known. For
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