  The available theoretical approaches aiming at describing Dynamic Nuclear
spin Polarization (DNP) in solutions containing molecules of biomedical
interest and paramagnetic centers are not able to model the behaviour observed
upon varying the concentration of trityl radicals or the polarization
enhancement caused by moderate addition of gadolinium complexes. In this
manuscript, we first show experimentally that the nuclear steady state
polarization reached in solutions of pyruvic acid with 15 mM trityl radicals is
substantially independent from the average internuclear distance. This
evidences a leading role of electron (over nuclear) spin relaxation processes
in determining the ultimate performances of DNP. Accordingly, we have devised a
variant of the Thermal Mixing model for inhomogenously broadened electron
resonance lines which includes a relaxation term describing the exchange of
magnetic anisotropy energy of the electron spin system with the lattice. Thanks
to this additional term, the dependence of the nuclear polarization on the
electron concentration can be properly accounted for. Moreover, the model
predicts a strong increase of the final polarization on shortening the electron
spin-lattice relaxation time, providing a possible explanation for the effect
of gadolinium doping.
