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^{1}, Yang Gao

^{2}, Arjen H. Bos

^{1}, Arthur M. de Jong

^{1}, Martien A. Hulsen

^{2}, Jaap M. J. den Toonder

^{2}and Menno W. J. Prins

^{1,3,a)}

### Abstract

The application of magnetic particles in biomedical research and in-vitro diagnostics requires accurate characterization of their magnetic properties, with single-particle resolution and good statistics. Here, we report intra-pair magnetophoresis as a method to accurately quantify the field-dependent magnetic moments of magnetic particles and to rapidly generate histograms of the magnetic moments with good statistics. We demonstrate our method with particles of different sizes and from different sources, with a measurement precision of a few percent. We expect that intra-pair magnetophoresis will be a powerful tool for the characterization and improvement of particles for the upcoming field of particle-based nanobiotechnology.

This project was funded by the Dutch Technology Foundation (STW) under grant (No. 10458).

### Key Topics

- Magnetic moments
- 11.0
- Magnetization measurement
- 10.0
- Magnetic fields
- 7.0
- Statistical properties
- 7.0
- Magnetic moments measurement
- 6.0

## Figures

Sketch of the intra-pair magnetophoresis methodology. (a) The separation S of magnetic particle pairs due to magnetic dipole-dipole interactions is measured in (b) out-of-plane and (c) in-plane magnetic fields. (d) Repeated separation and rejoining of magnetic particles S (black line) at different field strengths (blue line) with alternating in-plane and out-of-plane orientation (red line). (e) Microscopy images of M-270 superparamagnetic particles at different times, upon application of an out-of-plane magnetic field at t = 0. The image is a zoom-in of the total field of view.

Sketch of the intra-pair magnetophoresis methodology. (a) The separation S of magnetic particle pairs due to magnetic dipole-dipole interactions is measured in (b) out-of-plane and (c) in-plane magnetic fields. (d) Repeated separation and rejoining of magnetic particles S (black line) at different field strengths (blue line) with alternating in-plane and out-of-plane orientation (red line). (e) Microscopy images of M-270 superparamagnetic particles at different times, upon application of an out-of-plane magnetic field at t = 0. The image is a zoom-in of the total field of view.

Intra-pair separation S as a function of time of a single pair of M-270 particles, determined for different field strengths (open circles). The solid curves correspond to fits based on the solution of the equation of motion [Eq. (2) ]. The inset shows the same data, but now with the fifth power of the intra-pair separation (S 5) on the y-axis. The dynamic range of the intra-pair force in the experiment is on the order of 103 (ranging from ∼10 pN to ∼0.01 pN at 16 mT, obtained using Eq. (2) for the smallest and the largest distance).

Intra-pair separation S as a function of time of a single pair of M-270 particles, determined for different field strengths (open circles). The solid curves correspond to fits based on the solution of the equation of motion [Eq. (2) ]. The inset shows the same data, but now with the fifth power of the intra-pair separation (S 5) on the y-axis. The dynamic range of the intra-pair force in the experiment is on the order of 103 (ranging from ∼10 pN to ∼0.01 pN at 16 mT, obtained using Eq. (2) for the smallest and the largest distance).

Magnetization curves determined for three individual particle pairs (M-270, denoted by open squares, open diamonds, and open circles; the error-bars are shown within the symbols). The data for all three pairs were collected within a timespan of 40 s. The solid circles correspond to VSM measurements (vibrating sample magnetometry) performed on an ensemble of the same batch of particles. The curves correspond to a log-normal distribution-weighted sum of Langevin curves. The best fitting log-normal distribution functions f(mgrain) of the magnetic moments of the particle grains are shown in the inset for the four experimental data-sets. From repeated measurements on the same particles, the error in particle magnetic moment per measurement point is found to be about 4%.

Magnetization curves determined for three individual particle pairs (M-270, denoted by open squares, open diamonds, and open circles; the error-bars are shown within the symbols). The data for all three pairs were collected within a timespan of 40 s. The solid circles correspond to VSM measurements (vibrating sample magnetometry) performed on an ensemble of the same batch of particles. The curves correspond to a log-normal distribution-weighted sum of Langevin curves. The best fitting log-normal distribution functions f(mgrain) of the magnetic moments of the particle grains are shown in the inset for the four experimental data-sets. From repeated measurements on the same particles, the error in particle magnetic moment per measurement point is found to be about 4%.

Histograms of the pair-averaged and single particle magnetic moments. (a) Measured distributions of pair-averaged magnetic moments for the different types of magnetic particles, i.e., M-270, MyOne, and Micromer particles at a field of 13 mT. Each histogram corresponds to about 50 individual measurements on different particle pairs. The curves are obtained by calculating the pair averaged moment distribution from the single particle moment distributions in panel (b). (b) Deduced single particle moment distributions. Asymmetric peak functions are shown of single particle moment distributions which lead to the optimal fit of the measured pair-based distributions in panel (a).

Histograms of the pair-averaged and single particle magnetic moments. (a) Measured distributions of pair-averaged magnetic moments for the different types of magnetic particles, i.e., M-270, MyOne, and Micromer particles at a field of 13 mT. Each histogram corresponds to about 50 individual measurements on different particle pairs. The curves are obtained by calculating the pair averaged moment distribution from the single particle moment distributions in panel (b). (b) Deduced single particle moment distributions. Asymmetric peak functions are shown of single particle moment distributions which lead to the optimal fit of the measured pair-based distributions in panel (a).

## Tables

Magnetic properties of three different particle types quantified by intra-pair magnetophoresis.

Magnetic properties of three different particle types quantified by intra-pair magnetophoresis.

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