title: High-Sensitivity Measurement of Density by Magnetic Levitation.
abstract: This paper presents methods that use Magnetic Levitation (MagLev) to measure very small differences in density of solid diamagnetic objects suspended in a paramagnetic medium. Previous work in this field has shown that, while it is a convenient method, standard MagLev (i.e., where the direction of magnetization and gravitational force are parallel) cannot resolve differences in density <10(-4) g/cm(3) for macroscopic objects (>mm) because (i) objects close in density prevent each other from reaching an equilibrium height due to hard contact and excluded volume, and (ii) using weaker magnets or reducing the magnetic susceptibility of the medium destabilizes the magnetic trap. The present work investigates the use of weak magnetic gradients parallel to the faces of the magnets as a means of increasing the sensitivity of MagLev without destabilization. Configuring the MagLev device in a rotated state (i.e., where the direction of magnetization and gravitational force are perpendicular) relative to the standard configuration enables simple measurements along the axes with the highest sensitivity to changes in density. Manipulating the distance of separation between the magnets or the lengths of the magnets (along the axis of measurement) enables the sensitivity to be tuned. These modifications enable an improvement in the resolution up to 100-fold over the standard configuration, and measurements with resolution down to 10(-6) g/cm(3). Three examples of characterizing the small differences in density among samples of materials having ostensibly indistinguishable densities-Nylon spheres, PMMA spheres, and drug spheres-demonstrate the applicability of rotated Maglev to measuring the density of small (0.1-1 mm) objects with high sensitivity. This capability will be useful in materials science, separations, and quality control of manufactured objects.
authors.affiliation: Department of Chemistry and Chemical Biology, ‡Wyss Institute for Biologically Inspired Engineering, and §Kavli Institute for Bionano Science and Technology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: Alex
authors.initials: A
authors.lastname: Nemiroski
authors.affiliation: Department of Chemistry and Chemical Biology, ‡Wyss Institute for Biologically Inspired Engineering, and §Kavli Institute for Bionano Science and Technology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: A A
authors.initials: AA
authors.lastname: Kumar
authors.affiliation: Department of Chemistry and Chemical Biology, ‡Wyss Institute for Biologically Inspired Engineering, and §Kavli Institute for Bionano Science and Technology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: Siowling
authors.initials: S
authors.lastname: Soh
authors.affiliation: Department of Chemistry and Chemical Biology, ‡Wyss Institute for Biologically Inspired Engineering, and §Kavli Institute for Bionano Science and Technology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: Daniel V
authors.initials: DV
authors.lastname: Harburg
authors.affiliation: Department of Chemistry and Chemical Biology, ‡Wyss Institute for Biologically Inspired Engineering, and §Kavli Institute for Bionano Science and Technology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: Hai-Dong
authors.initials: HD
authors.lastname: Yu
authors.affiliation: Department of Chemistry and Chemical Biology, ‡Wyss Institute for Biologically Inspired Engineering, and §Kavli Institute for Bionano Science and Technology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: George M
authors.initials: GM
authors.lastname: Whitesides