An increasing number of promising applications for future technology is arising from size constraints in nanoparticles (NPs) and from the chemical manipulation of their surfaces. In this work, we analyse the finite-size and surface effects on polyacrylic acid-coated Fe₃O₄ NPs and oleic acid-coated γ-Fe₂O₃ NPs by studying their magnetization curves at different temperatures. The measured thermal dependence of the saturation magnetization is no longer explained by the typical T^3/2 Bloch law, yielding higher values than those expected for its exponent. When incorporated in polymeric matrixes to form magnetic transparent nanocomposites, the oleic acid-coated γ-Fe₂O₃ NPs also deviate from Bloch’s law, but following the opposite trend observed in free coated NPs.

In this paper we compare a single reservoir model and a trip-based model under piecewise linear MFD and a piecewise constant demand. These assumptions allow to establish the exact solution of the accumulation-based model, and continuous approximations of the trip-based model at any order using Taylor series