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

Abstract

Brownian magnetic nanoparticles present a large sensitivity to AC fields, opening new routes to bio-sensing by bio-functionalized nanoparticles. The integration of theory and experiment permit to transduce any magnetic response (via susceptibility, harmonics or hysteresis area) to extract relevant system's parameters (such as particle size, solvent viscosity, temperature). Parameter estimators based on linear response theory are easy to implement, but their sensitivity and resolution is 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 relation is available. Here we have solved this dilemma by deriving an empirical analytical relation for the magnetic hysteresis area which is valid under arbitrary field intensity and frequency, thus avoiding the need of calibration. This universal relation matches within 1% 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 relation, we have built an extremely fast automated-searching algorithm which simultaneously estimates several system's parameters by fitting experimental data for the area (at varying intensity and frequency). 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 \emph{stand-alone technique} able to determine, with outstanding accuracy, particle size, polydispersity, concentration, magnetic moment as well as solvent viscosity and temperature. We validate this method in biosensing protocols, by determining nanometer-size variations in bio-functionalized nanoparticles upon protein-target recognition.