  We discuss the polarization dynamics during solid effect dynamic nuclear
polarization (DNP) in a central spin model that consists of an electron
surrounded by many nuclei. To this end we use a recently developed formalism
and validate first its performance by comparing its predictions to results
obtained by solving the Liouville von Neumann master equation. The use of a
Monte Carlo method in our formalism makes it possible to significantly increase
the number of spins considered in the model system. We then analyse the
dependence of the nuclear bulk polarization on the presence of nuclei in the
vicinity of the electron and demonstrate that increasing the minimal distance
between nuclei and electrons leads to a rise of the nuclear bulk polarization.
These observations have implications for the design of radicals that can lead
to impoved values of nuclear spin polarization. Furthermore, we discuss the
potential to extend our formalism for more complex spin systems such as cross
effect DNP.
