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

摘要

Aiming to analyze relevant aspects of interacting magnetic nanoparticle systems (frequently called interactingsuperparamagnets), a model is built from magnetic dipolar interaction and demagnetizing mean-field concepts.By making reasonable simplifying approximations, a simple and useful expression for effective demagnetizingfactors is achieved, which allows the analysis of uniform and nonuniform spatial distributions of nanoparticles,in particular the occurrence of clustering. This expression is a function of demagnetizing factors associatedwith specimen shape and clusters shape, and of the mean distances between near neighbor nanoparticles andbetween clusters, relative to the characteristic sizes of each of these two types of objects, respectively. Themodel explains effects of magnetic dipolar interactions, such as the observation of apparent nanoparticlemagnetic moments smaller than real ones and approaching to zero as temperature decreases. It is shownthat by performing a minimum set of experimental determinations along principal directions of geometricallywell-defined specimens, model application allows retrieval of nanoparticle intrinsic properties, likemean volume,magnetic moment, and susceptibility in the absence of interactions. It also permits the estimation of meaninterparticle and intercluster relative distances, as well as mean values of demagnetizing factors associated withclusters shape. An expression for average magnetic dipolar energy per nanoparticle is also derived, which isa function of specimen effective demagnetizing factor and magnetization. Experimental test of the model wasperformed by analysis of results reported in the literature and of original results reported here. The first casecorresponds to oleic-acid-coated 8-nm magnetite particles dispersed in PEGDA-600 polymer, and the secondone to polyacrilic-acid-coated 13-nm magnetite particles dispersed in PVA solutions from which ferrogels werelater produced by a physical cross-linking route. In both cases, several specimens were studied covering arange of nanoparticle volume fractions between 0.002 and 0.046. Magnetic response is clearly different whenprism-shaped specimens are measured along different principal directions. These results remark the importanceof reporting complete information on measurement geometry when communicating magnetic measurementresults of interacting magnetic nanoparticles. Intrinsic nanoparticle properties as well as structural informationon particles spatial distribution were retrieved from our analysis in addition to, and in excellent agreement with,analysis previously performed by other authors and/or information obtained from FESEM images. In the studiedsamples, nanoparticles were found to be in close contact to each other within almost randomly oriented clusters.Intercluster mean distance, relative to cluster size, was found to vary between 2.2 and 7.5, depending on particlesvolume fraction.