Generalized Scaling and the Master Variable for Brownian Magnetic Nanoparticle Dynamics.

Daniel B Reeves,John B Weaver,Yipeng Shi,Amitava Mukherjee

doi:10.1371/journal.pone.0150856

Abstract

Understanding the dynamics of magnetic particles can help to advance several biomedical nanotechnologies. Previously, scaling relationships have been used in magnetic spectroscopy of nanoparticle Brownian motion (MSB) to measure biologically relevant properties (e.g., temperature, viscosity, bound state) surrounding nanoparticles in vivo. Those scaling relationships can be generalized with the introduction of a master variable found from non-dimensionalizing the dynamical Langevin equation. The variable encapsulates the dynamical variables of the surroundings and additionally includes the particles’ size distribution and moment and the applied field’s amplitude and frequency. From an applied perspective, the master variable allows tuning to an optimal MSB biosensing sensitivity range by manipulating both frequency and field amplitude. Calculation of magnetization harmonics in an oscillating applied field is also possible with an approximate closed-form solution in terms of the master variable and a single free parameter.

Highlights

Biosensing and nanotechnologyThe ability to study the human body non-invasively, both for basic science and medicine, has historically been an excellent marker of scientific progress
The harmonics are unchanged by scaling the relaxation time when plotted against the master variable when fhτBi = hOi > 1
We showed by non-dimensionalizing the Langevin equation that, in the regime of large unitless field compared to relaxation time oscillating field period (ξ0 > O), the dynamics of Brownian magnetic nanoparticles are determined by a single master variable, A, that incorporates most typically considered nanoparticle properties as well as applied magnetic field properties

Summary

Introduction

The ability to study the human body non-invasively, both for basic science and medicine, has historically been an excellent marker of scientific progress. From the first clinical X-ray imaging in 1896 [1] to the first human body MRI in 1977 [2], we have arrived in the era of nanotechnology, allowing researchers to generate many types of nanoscopic sensors that can enter the body themselves and return information with relative non-toxicity. The magnetization response of Brownian magnetic nanoparticles in an oscillating magnetic field contains extensive information characterizing the microenvironment around the particles. In contrast to Néel rotation where the internal magnetic dipole rotates, Brownian particles rotate mechanically, coupling their motion to their surroundings [3].

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Conclusion