Fast and accurate characterization of bioconjugated particles and solvent properties by a general nonlinear analytical relationship for the AC magnetic hysteresis area

Brownian magnetic nanoparticles present a large sensitivity to AC fields, opening new routes to bio-sensing using bio-functionalized nanoparticles. The integration of theory and experiment permits the transduction of any magnetic response (via susceptibility, harmonics or hysteresis area) to extract relevant system's parameters (such as particle size, solvent viscosity, and temperature). Parameter estimators based on linear response theory are easy to implement, but their sensitivity and resolution are limited by construction. Nonlinear responses allow for much higher sensitivities, but demand a significant cost in complex simulations to fit the experiments, because no analytical relationship is available. Here we have solved this dilemma by deriving an empirical analytical relationship for the magnetic hysteresis area which is valid under the arbitrary field intensity and frequency, thus avoiding the need for calibration. This universal relationship matches within 1% of the outcome of the nonlinear Fokker-Planck equation and has been validated against detailed Brownian dynamic simulations and controlled experiments. Using this nonlinear magnetic hysteresis area relationship, we have built an extremely fast automated searching algorithm that simultaneously estimates several system parameters by fitting experimental data for the area (at varying intensities and frequencies). The searching scheme starts with a robust and flexible stochastic method (parallel tempering Monte Carlo) followed by an accurate deterministic multi-variable minimization (Gauss-Newton) to match experimental areas within ∼1% deviation. This integrated approach upgrades AC-magnetometry into a stand-alone technique able to determine, with outstanding accuracy, particle size, polydispersity, concentration, and magnetic moment, as well as solvent viscosity and temperature. We validated this method in biosensing protocols by determining nanometer-size variations in bio-functionalized nanoparticles upon protein target recognition.