Low-gradient magnetophoresis through field-induced reversible aggregation

Recent experiments (Yavuz, C. T. et A, Science 2006, 314, 964) show the possibility of low gradient magnetophoretic separation of superparamagnetic nanoparticles in aqueous solution, a process with broad potentially important applications ranging from biomedicine to environmental waste and pollutants removal. Here, we show that the key to low gradient magnetophoresis is the existence of a cooperative mechanism (reversible aggregation) which fuels the magnetophoresis process. The interplay between the different factors determining low gradient magnetophoresis (magnetization of particles, size,...) is consistently described by a magnetic analogous to the Bjerrum length concept. This concept allows us to formulate a simple criterion predicting the onset of low gradient magnetophoresis separation as a function of the sample properties (e.g., minimum particle radius). These predictions are in agreement with experimental observations. The kinetics of the process depends not only on the properties of the particles but also on concentration. The observed separation times are orders of magnitude shorter than the predictions of present models based on the approximation of noninteracting particles. The separation times of samples with different concentrations and different particles can be described with a unique curve depending on the magnetic Bjerrum length and the concentration.