Dipolar interaction and demagnetizing effects in magnetic nanoparticle dispersions: Introducing the mean-field interacting superparamagnet model

A model is developed with the aim of analyzing interacting superparamagnets. Model is built from magnetic dipolar interaction and demagnetizing mean field concepts. A useful expression for effective demagnetizing factors is achieved, which allows for the analysis of non uniform spatial distributions of nanoparticles. This expression is a function of demagnetizing factors associated with specimen and clusters shapes, and of the mean distances between near neighbor nanoparticles and between clusters, relative to the characteristic sizes of each of these two types of objects, respectively. It explains effects of magnetic dipolar interactions such as the observation of apparent nanoparticle magnetic-moments smaller than real ones. It is shown that by performing a minimum set of experimental determinations, model application allows retrieval of intrinsic properties, like magnetic moment and susceptibility in the absence of interactions. It also permits the estimation of mean interparticle and intercluster relative distances, and of demagnetizing factors associated with clusters shape. An expression for magnetic dipolar energy per nanoparticle is also derived. Model experimental test was performed by analysis of results reported in the literature and of original results. They correspond to magnetite particles dispersed in PEGDA-600 polymer, and in PVA ferrogels. Experimental results display different magnetic response when prism shaped specimens are measured along principal directions. Intrinsic properties and structural information were retrieved from the analysis, in excellent agreement with information obtained from FESEM images. In the studied samples nanoparticles were found to be in close contact to each other within almost randomly oriented clusters. Intercluster mean relative-distance was found to vary between 2.2 and 7.5, depending on particles volume fraction.