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Frequency mixing magnetic detection (FMMD) has been widely utilized as a measurement technique in magnetic immunoassays. It can also be used for the characterization and distinction (also known as “colourization”) of different types of magnetic nanoparticles (MNPs) based on their core sizes. In a previous work, it was shown that the large particles contribute most of the FMMD signal. This leads to ambiguities in core size determination from fitting since the contribution of the small-sized particles is almost undetectable among the strong responses from the large ones. In this work, we report on how this ambiguity can be overcome by modelling the signal intensity using the Langevin model in thermodynamic equilibrium including a lognormal core size distribution fL(dc,d0,σ) fitted to experimentally measured FMMD data of immobilized MNPs. For each given median diameter d0, an ambiguous amount of best-fitting pairs of parameters distribution width σ and number of particles Np with R2 > 0.99 are extracted. By determining the samples’ total iron mass, mFe, with inductively coupled plasma optical emission spectrometry (ICP-OES), we are then able to identify the one specific best-fitting pair (σ, Np) one uniquely. With this additional externally measured parameter, we resolved the ambiguity in core size distribution and determined the parameters (d0, σ, Np) directly from FMMD measurements, allowing precise MNPs sample characterization.
Dual frequency magnetic excitation of magnetic nanoparticles (MNP) enables enhanced biosensing applications. This was studied from an experimental and theoretical perspective: nonlinear sum-frequency components of MNP exposed to dual-frequency magnetic excitation were measured as a function of static magnetic offset field. The Langevin model in thermodynamic equilibrium was fitted to the experimental data to derive parameters of the lognormal core size distribution. These parameters were subsequently used as inputs for micromagnetic Monte-Carlo (MC)-simulations. From the hysteresis loops obtained from MC-simulations, sum-frequency components were numerically demodulated and compared with both experiment and Langevin model predictions. From the latter, we derived that approximately 90% of the frequency mixing magnetic response signal is generated by the largest 10% of MNP. We therefore suggest that small particles do not contribute to the frequency mixing signal, which is supported by MC-simulation results. Both theoretical approaches describe the experimental signal shapes well, but with notable differences between experiment and micromagnetic simulations. These deviations could result from Brownian relaxations which are, albeit experimentally inhibited, included in MC-simulation, or (yet unconsidered) cluster-effects of MNP, or inaccurately derived input for MC-simulations, because the largest particles dominate the experimental signal but concurrently do not fulfill the precondition of thermodynamic equilibrium required by Langevin theory.